Trojan: They usually obtain system privileges, destory system, steal private user infomation, download/drop other malware
Backdoor: Hackers can use this to monitor & control your computer silently.
Worm: They spread through networks and replicate themselves on other connected computers, sometimes they steal private user infomation.
Virus: Most of them can infect other files, but most of the infected files can be restored to their normal conditions after the virus is cleared.
Exploit: They use the leaks of operating system or programs to get high privilege or attack your computer.
Hacktool: Hackers can use this to attack your computer, start DDoS attack, scan for leaks in computer, etc.
Adware: Usually bundled with free software, pop-up annoying ads, slow down computer speed.
PUA: Possibly Unwanted Application, these software usually have not very good reputation, bundled in some silent installers.
Macro: Macro viruses are a type of malware stored in Microsoft Office file/template macros. Once this file is opened, the macro will be run, activating the macro virus so it will reside in the Normal template. Afterwards, all auto-saved files will be infected with this macro virus.