Mal- means bad/evil/intended to harm, so malware is any program that has evil intent.
Ad- for advertisement, so any program designed to display adverts, usually a banner in an ad-supported program or in pop-up windows which can appear unexpectedly at any time. Adware is often criticised for installing without explicit consent (sneakily), using system resources and resisting removal, although it may not have evil intent. On the other hand, some adware is installed without any consent at all (drive by download) and may use rootkit technology to hide itself and prevent removal- in which case it is definitely malware.
Spy- for observe covertly to obtain information. There are two types of spyware here: one observes what websites you visit and searches you make on the internet in order to target advertising, the other steals personal information like credit card numbers, bank details etc. The first is obviously associated with adware, the second has criminal intent and is definitely evil.
http://www.geocities.com/dontsurfinthenude/spyware.htm
http://www.geocities.com/dontsurfinthenude/spysymptoms.htm
http://www.geocities.com/dontsurfinthenude/spyprotection.htm
A spyware scanner is definitely a good extra layer of protection, but only one spyware scanner with resident protection is advisible. (You can have as many on-demand scanners as you want.)
One of these: Spyware Doctor, CounterSpy, SpySweeper, AVG Anti-Spyware- all pay products- Spyware Terminator, SuperAntiSpyware*, Windows Defender- free products.
As many as you like of these: AVG Anti-Spyware Free, a-Squared Free, Ad-Aware Free, Spybot Search & Destroy.
So your set up is fine with Spyware Doctor and Ad-Aware.
*This program doesn’t have resident protection, but it does have a service which remains active even when not running a scan, and which might conflict with other programs. If anybody knows better, please feel free to comment.
EDIT: Typo