The only real difference is that some security applications may leave remnants or orphaned files related to the infection (as most infections are normally created using a number of files).
Again, it really shouldn't make much difference though because as long as these files are no longer "active" or able to re-spawn the infection on your PC, then you'll be safe anyway.
This can sometimes be why certain security apps will scan your computer and claim you're infected, just because you have a file related to an infection on your disk somewhere - even though the infection was already successfully removed.