The term malware (short for malicious software) usually refers to any file that intentionally alters your computer (usually without your permission) in order to impair functionality, control your system, breach your privacy, advertise, or produce some other unwanted behavior.
Malware is a general term that encompasses many types of malicious programs, including viruses, trojan horses (“trojans”), rogues, spyware, keyloggers, worms, rootkits, dialers, backdoors, etc.
There is a good explanation of malware on wikipedia, including links to descriptions of malware types.
Currently, most scanning programs check for all types of malware regardless of the term used their name. For example, Comodo antivirus scans for all types of malware, even though its name is “antivirus”. Superantispyware checks for trojans, rootkits, rogues, keyloggers, spyware, etc. even though its name is “antispyware”. Virustotal.org and virscan.org (see below) scan for all types of malware, including viruses and trojans.
I agree. A scanner may detect a false positive (the scanner flags a file as malicious, when the file is actually harmless). Deleting a false positive can cause problems with your computer. If a program detects a file as malicious, I recommend that you download the file to a site such as www.virustotal.com or www.virscan.org, which will scan the file with a bunch of different anti-malware engines. If you suspect that the file is malicious (and not a false positive) based on the results from one of these on-line scans, then quarantine the threat (do not delete it). Quarantining the threat will disable it. Once the file is quarantined, you can see how your computer functions. If the file was not infected or the file was necessary for your computer to function, then you can restore the file (if you deleted the file, you can never get the file back and you may not be able to salvage your system!). If you are not sure what to do, you can always ask for help on one of the many user forums (including this one) before you take action on a potential threat.
Johnzbzb, I suspect that the “traces of Trojan.Win32.Generic!BT” on your system were false positives; however, it is impossible to know for sure because the files have been deleted.
Hope that answers your questions,
P.S. also see my response to your other post.