The main difference is with a flush trim bit (bearing on the bottom) the pattern or surface you are following is on that side. If you are using a pattern bit (bearing on the bit shaft) the pattern will be on the same side as the router. In some cases it doesn't make any difference which one you use. On a router table I prefer to use a trim bit if I can for safety reasons. In that case there are no cutting edges exposed during the cut. The bearing is in between me and the cutters. If you were routing out the lip on a home made router table for the plate to sit on and you had a template to follow you would be using the pattern bit as an example. So it all depends on the circumstances which one is appropriate.
Someone I consider a master woodworker once told me that a master woodworker is not someone who never makes mistakes. He is someone who is able to cover them up so that no one can tell.