• Screening Router Firewalls:
It's a software base firewall available in Router provides only light filtering.

• Computer-based Firewall:
It's a firewall stored in server with an existing Operating System like Windows and UNIX.

• Hardware base Firewall:
Its device like box allows strong security from public network. Mostly used by big networks.

• Proxy Server:

Proxy server allows all clients to access Internet with different access limits. Proxy server has its own firewall which filters the all packet from web server.

UFW, or uncomplicated firewall, is a frontend for managing firewall rules in Arch Linux, Debian or Ubuntu. UFW is used through the command line (although it has GUIs available), and aims to make firewall configuration easy (or, uncomplicated).

Before You Begin

To install UFW follow this link for the command : 

Firewalls and proxy servers both can help you block viruses and other forms of malware from infecting your computers. A firewall can block ports commonly used by malicious viruses and worms. You can also use the firewall to specify which ports can be open. Common ports that are usually open are HTTP (port 80), SMTP (port 25) and POP3 (port 110). You may wish to leave certain other ports open as well, while closing other ports. Proxy servers, on the other hand, create a barrier by being the "middleman" that sits between your network and the Internet. Users outside your network can see only your proxy server, while those inside the network can access the Internet only by passing through the proxy. This limits the window of opportunity through which viruses and worms can enter.

Blocking Programs

A firewall can prevent programs from running on your computer. A proxy server cannot do this. Specific programs such as games and instant messaging applications can be blocked by the firewall. You can also block services and create exceptions for programs that you wish to allow.

Blocking Websites

You can block websites through a firewall, but you may bring your Internet access down. A firewall can block port 80, which the HTTP protocol uses to serve Web pages, but if you do this, you won't be able to access any websites at all. A proxy server is better suited to this task in that it is more discriminating in filtering websites. For example, you can choose to block all social networking sites during office hours but allow access to them during lunch breaks and after hours. Some proxy servers have the option to categorize websites, making it easier for you to block all entertainment websites or all adult websites without having to type Web addresses one by one.

Functional Differences

A firewall essentially blocks communication, while a proxy server simply redirects it. When you cannot access a website because a proxy is blocking it, it is not exactly blocking the communication. When a user tries to access a disallowed website, the proxy server has an internal mechanism that redirects those requests to a Web page in your network. It appears to the user that the website is blocked, but the request was simply redirected to point to something else.

Other Proxy Server Functions

A proxy server is not only capable of redirecting websites, but it can also cache them. If users access a particular website every day, instead of fetching pages from the site again and again, the proxy server simply sends cached information to the users. This considerably reduces network traffic because your request won't have to go out to the Internet every time.

reference : https://yourbusiness.azcentral.com/difference-between-firewall-proxy-server-20024.html