Adware, spyware and computer virus are not the same and do not harm computers in the same way. The differences between them are the reason that your computer protection must have both anti-virus and anti-malware protection.
Viruses are programs that can replicate themselves inside a host system. They are contracted by contact with an infected system or shared file. The replication of the virus is different for each virus.
Spyware is software that is designed to create channels for another user to communicate with the computer. Spyware tracks the web sites you visit and communicates the information to advertisers which open the door to unwanted emails and pop-ups.
Adware, is a form of freeware attached to a program and is installed automatically once that particular program or software is downloaded. Adware communicates to the source system sending information about your browsing habits and is the source of most SPAM in emails.