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A battery is a device that stores chemical energy, and converts it to electricity. This is known as electrochemistry and the system that underpins a battery is called an electrochemical cell. A battery can be made up of one or several (like in Volta's original pile) electrochemical cells. Each electrochemical cell consists of two electrodes separated by an electrolyte.

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Batteries play a critical role in our lives. It is hard to imagine a life without the usage of batteries. In the last few decades, the usage of batteries in consumer applications has been exponential. Batteries are being used in a huge number of appliances. Some of them are mentioned below:

Portable Electronic Devices: Watches, Cameras, Mobile Phones, Laptops, Camcorders, Calculators, testing equipment (Multimeters).

Entertainment: Radios, MP3 players, CD Players, all infrared remote controls, toys, games, keyboards.

Household: Clocks, Alarms, Smoke Detectors, Flash lights, UPS, Emergency lights, tooth brushes, hair trimmers and shavers, Blood Pressure Monitors, Hearing Aids, pacemakers, portable power tools (drills, screw driver).

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A Primary Battery is one of the simple and convenient sources of power for several portable electronic and electrical devices like lights, cameras, watches, toys, radios etc. As they cannot be recharged electrically, they are of “use it and when discharged, discard it” type.

Usually, primary batteries are inexpensive, light weight, small and very convenient to use with relatively no or less maintenance. Majority of the primary batteries that are used in domestic applications are single cell type and usually come in cylindrical configuration (although, it is very easy to produce them in different shapes and sizes).

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zinc–carbon (Leclanché) cells

alkaline zinc–manganese dioxide cells

metal–air-depolarized batteries

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A Secondary Battery is also called as Rechargeable Battery as they can be electrically recharged after discharge. The chemical status of the electrochemical cells can be “recharged” to their original status by passing a current through the cells in the opposite direction of their discharge.
The four major types of secondary batteries are:

Lead – Acid Batteries

Nickel – Cadmium Batteries

Nickel – Metal Hydride Batteries

Lithium – Ion Batteries

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A fuel cell is an electrochemical cell that converts the chemical energy of a fuel (often hydrogen) and an oxidizing agent (often oxygen) into electricity through a pair of redox reactions. Fuel cells are different from most batteries in requiring a continuous source of fuel and oxygen (usually from air) to sustain the chemical reaction, whereas in a battery the chemical energy usually comes from metals and their ions or oxides that are commonly already present in the battery, except in flow batteries. Fuel cells can produce electricity continuously for as long as fuel and oxygen are supplied.

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Fuel cells can be used in a wide range of applications, providing power for applications across multiple sectors:

transportation

industrial/commercial/residential buildings

long-term energy storage for the grid in reversible systems.

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Some differences of batteries and fuel cells are the following:

In fuel cell, reactants are constantly supplying, whereas in battery reactants are stored inside the battery only.

Fuel cell is an open system as reactants are stored outside while battery is a closed system.

Fuel cell works as long as fuel is supplied while battery require regular replacements.

Fuel cell requires more space as reactants stored outside while battery requires less space.

Fuel cells can supply power for indefinite length of time while batteries supply power for definite length of time.

Amount of heat generated in fuel cells are much more compared to batteries.

In fuel cells, no changes occur in chemical composition of electrolyte, while chemical changes occur in batteries.

By products must be constantly removed (Water) from fuel cells unlike batteries.

Fuel cells are more expensive than batteries.

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Some similarities of batteries and fuel cells are the following:

Both are a collection of individual cells that work to cleanly and efficiently convert chemical energy in hydrogen-rich fuels into electricity.

Both stores an energy source and converts it into electrical energy.

Both are galvanic cells that directly generate electricity through electrochemical reactions.

Both have an anode and a cathode in contact with an electrode.

Both are electrochemical devices.

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nickel-cadmium (NiCd)

lead acid

lithium ion batteries

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Polymer electrolyte membrane (PEM) fuel cells also called as proton exchange membrane fuel cells, deliver high power density and offer the advantages of low weight and volume compared with other fuel cells. PEM fuel cells use a solid polymer as an electrolyte and porous carbon electrodes containing a platinum or platinum alloy catalyst. They need only hydrogen, oxygen from the air, and water to operate. They are typically fueled with pure hydrogen supplied from storage tanks or reformers.

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Most fuel cells are powered by hydrogen, which can be fed to the fuel cell system directly or can be generated within the fuel cell system by reforming hydrogen-rich fuels such as methanol, ethanol, and hydrocarbon fuels. Direct methanol fuel cells (DMFCs), however, are powered by pure methanol, which is usually mixed with water and fed directly to the fuel cell anode.

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Alkaline fuel cells (AFCs) were one of the first fuel cell technologies developed, and they were the first type widely used in the U.S. space program to produce electrical energy and water on-board spacecraft. These fuel cells use a solution of potassium hydroxide in water as the electrolyte and can use a variety of non-precious metals as a catalyst at the anode and cathode.

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Phosphoric acid fuel cells (PAFCs) use liquid phosphoric acid as an electrolyte, the acid is contained in a Teflon-bonded silicon carbide matrix and porous carbon electrodes containing a platinum catalyst. The PAFC is considered the "first generation" of modern fuel cells. It is one of the most mature cell types and the first to be used commercially. This type of fuel cell is typically used for stationary power generation, but some PAFCs have been used to power large vehicles such as city buses.

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Molten carbonate fuel cells (MCFCs) are currently being developed for natural gas and coal-based power plants for electrical utility, industrial, and military applications. MCFCs are high-temperature fuel cells that use an electrolyte composed of a molten carbonate salt mixture suspended in a porous, chemically inert ceramic lithium aluminum oxide matrix.

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Solid oxide fuel cells (SOFCs) use a hard, non-porous ceramic compound as the electrolyte. SOFCs are around 60% efficient at converting fuel to electricity. In applications designed to capture and utilize the system's waste heat (co-generation), overall fuel use efficiencies could top 85%. SOFCs operate at very high temperatures, as high as 1,000°C (1,830°F). High-temperature operation removes the need for precious-metal catalyst, thereby reducing cost. It also allows SOFCs to reform fuels internally, which enables the use of a variety of fuels and reduces the cost associated with adding a reformer to the system.

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Reversible fuel cells produce electricity from hydrogen and oxygen and generate heat and water as byproducts, just like other fuel cells. However, reversible fuel cell systems can also use electricity from solar power, wind power, or other sources to split water into oxygen and hydrogen fuel through a process called electrolysis. Reversible fuel cells can provide power when needed, but during times of high power production from other technologies (such as when high winds lead to an excess of available wind power), reversible fuel cells can store the excess energy in the form of hydrogen. This energy storage capability could be a key enabler for intermittent renewable energy technologies.

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https://www.science.org.au/curious/technology-future/batteries

https://www.electronicshub.org/types-of-batteries/#Different_Types_of_Batteries

https://en.wikipedia.org/wiki/Fuel_cell

https://www.energy.gov/eere/fuelcells/fuel-cells

https://www.technology.matthey.com/resources/view-questions-answers/fuel-cells-batteries-similar/

https://www.sciencedirect.com/topics/earth-and-planetary-sciences/primary-battery

https://www.energy.gov/eere/fuelcells/types-fuel-cells