resting vs proofing - are they the same thing? my croissants keep coming out flat

They're completely different processes, and mixing them up gives exactly the flat greasy croissants you're describing.

Resting is for the gluten and the butter - cold, tight dough relaxing so you can roll again without it fighting back. It happens COLD. And for croissant dough specifically, rest in the freezer, not the fridge. In the fridge the yeast keeps slowly fermenting the whole time and fills your lamination with gas.

Proofing is the yeast working. That's shaped croissants in a warm spot, around 25-27°C, for 2-3 hours until doubled. They should jiggle like set jelly when you shake the tray - that jiggle is the test, not the clock.

So: laminate (quick freezer chills whenever the dough warms), long freezer rest after the final fold, shape, warm proof till doubled, bake. If your proof happened cold, they went in underdeveloped = flat. If it happened too hot, the butter melted out before baking = greasy. From what you describe I'd bet on the proof.

Muffin tin works great, just use a paper liner - the caramelised sugar welds itself to bare metal. The ring matters more than people think btw, it holds the sugar-laminated dough together so it caramelises around itself into that tall whirl. On a flat tray it spreads into something closer to a palmier. Tasty, but not kouign-amann. Turn them out while still warm, before the caramel sets like glue.