Difference between de novo transcriptome assembly methods
Your intuition is correct. stringTie is just looking at clumps of alignments and how they might relate to each other (either due to spliced alignments or proximity). Trinity is doing the more computationally difficult task of finding parts of reads that overlap with each other and trying to link them together into longer sequences.

Whether it makes sense to use something like stringTie or not depends mostly on the quality of the reference sequence. If you're working on an organism with a high-quality reference sequence (pretty much anything with a lot of papers using it) then there's no reason to bother with Trinity. If your reference genome additionally has a high-quality annotation (human, mouse, etc.) then you should use it, as anything "novel" that the program is likely to output otherwise is probably just an artefact. If you either don't have an annotation or it's known to be highly problematic then it makes sense to omit it when using stringTie.

Without seeing evidence to the contrary, I don't buy the argument that using a good annotation is actually biasing the output in a problematic way. For well-studied organisms, anything reported as "novel" these days likely doesn't exist, or is otherwise so fleeting that it's biologically irrelevant. The arguments of bias sound like something that was come up with once someone didn't get as many "novel" results as they were hoping.