Let us understand Firewalls, anti-malware and anti-virus software a little better here.

Firewalls
Firewalls are security systems employed in networks to control outgoing/incoming traffic. The firewalls are responsible for determining whether data packets will be allowed through the network or not. Such factors are determined by a set of rules that have been employed in the firewalls.
A lot of operating systems include software-based of firewalls by default in order to offer protection from public internet threats. Furthermore, a lot of routers consist of firewall components and a lot of firewalls are responsible for basic routing function too. Following are the types of firewalls based on the level at which communication is happening.

Network Layer: This firewall is also known as packet filter and works at very low level of TCP/IP protocol stack. The firewall allows only those packets to get through that fulfill a specific rule set. These rules are either defined by administrator or set by default.
Application Layer: This firewall works on TCP/IP application level. At this level the firewall can inspect all packets and prevent or restrict spread of Trojans and worms.
Proxies may also act as firewalls. Such servers may respond to input packets and block other packets. It acts as a gateway from one to another network for any particular application.

Anti-Malware
Anti-malware programs are those that prevent malware from entering into a computer or detect and remove/repair it. It works in two ways:
First, it may work in real time and continue to scan all the incoming network data for threats. If any threat is found, it may block it or prompt for an action by a user. This is similar to the working of any antivirus software

Another type of anti-malware works on-demand for those malicious software that have been existing on the computer. This allows removal of already downloaded malware programs that may have infected operating system files, Windows registry or other installed programs. Once the scan is done, the user will get a prompt for further action. One can either keep the files and delete them manually or delete them in one go.

Antivirus software
Antivirus software is any program that allows a user to protect a computer system from virus and other malware attacks (as per the features included in the software). Antivirus system may offer protection from rootkits, malware, viruses, Trojans, worms, adware, spyware, phishing and many more malicious programs.

The antivirus scanner offers real-time protection or on-demand scan facility, if a user wishes to scan any particular sector of computer or external storage devices. It further offers protection from possible unwanted?threats. It may include heuristics for such protection.
These programs allow a user to enjoy smooth processing of computer and no attacks from viruses and other malware. It ensures that the data stored on the computer system is secured and that the user has nothing to worry about. Of course, one must have these installed on their PCs for maximum protection.