The Quick scan is essentially scanning those files which are targeted by malware (.exe, .com. dll, etc.) or if infected are an immediate risk. The Full System scan scans those same files and then a level where there is a lessor risk of infection or immediate risk if infected.
- With a resident on-access antivirus like avast, the need for frequent on-demand scans is much depreciated. For the most part the on-demand scan is going to be scanning files that would be otherwise be dormant or inert. If they were active files then the on-access file system shield would be scanning them before being created, modified, opened or executed.
I have avast set to do a scheduled weekly Quick scan, set at a time and day that I know the computer will be on. If for some reason my system wasn't on, no big deal I will catch up on the next scheduled scan.
I rarely ever do a Full System Scan.