Lanefan
Victoria Rules
I'd interpret "running on the fly" to mean you're winging everything with minimal if any prep other than maybe some setting basics: here's the town, here's the dungeon, but the dungeon isn't pre-written: you're making it up as the PCs explore it.I run on the fly because published adventures are too much work. And running on the fly does not mean you don't prep. You prep differently.
That isn't "homebrewing an adventure", though. Homebrewing an adventure means prepping it out to module-level detail (though maybe only on scraps of paper, doesn't have to be neatly formatted!) and then running it as written.