Malware: a general term refering to programs that are intentionally designed and distributed to damage and/or control computing devices and computer networks. Malware is short for Malicious Software.
The following terms refer to specific types of Malware:
Adware: Displays ads on your computer. Often installed along with free tools installed by undesirable sources.
Spyware: Tracks internet activities.
Virus: Contagious program or code that attaches itself to another piece of software, and then reproduces itself on the PC, network or to other computers via file transfers.
Worm: Self-replicating threat that destroys data and files on the computer.
Trojan: Trojans seek to discover information, like financial details. They can bring in other malicious code. Also used to take over resources to launch attacks against other devices.
Rootkit: Typically permits other information gathering malware in via back door.
Backdoors: Open a link onto a computer, providing a network connection for hackers or other malware.
Keyloggers: Records everything you type on your PC.
Ransomware: Locks out of computer or data on drives until user pays, generally via cyber-currency, to get a key. Even once you pay, you may never get a working key.
Browser hijacker: Redirects normal search activity to give results the hacker want you to see. Its intention is to make money off your web surfing. This can be as simple as sending ad-based content to being used to phish for your banking, or other, data.