Whats the difference between Anti-malware and antispyware ?
Malware is a portmanteau of the words "malicious" and "software". Spyware is a portmanteau of the words "spy" and "software".
In terms of the words themselves, there's little or no difference between them. One might describe spying as malicious, just as one might say that a backdoor application has spying capabilities.
In terms of technical differences, spyware is a class of malicious software that attempts to steal some kind of information from your computer, such as your personal information (e.g. name, address) or your credit card number, keystrokes, etc. It could also be something less overtly evil, such as reporting statistics about your browsing habits back to an advertising agency.
Anti-malware software usually targets the broad range of malicious software. It looks for the stuff that causes damage, loss, unauthorised access, or annoyance - essentially what a layman would refer to as "viruses".
Anti-spyware tends to focus on less of the "delete your entire hard disk" types of malicious software, and more on the "this will steal your personal information" stuff, including the less overtly evil stuff that I mentioned before.
If you're wondering if there's any difference in how they work, there pretty much isn't. The monitor file and application activities and look for things that match a signature or heuristic, then block them or report them to the user.