Conical is a standard type lighthouse, a circular base that gets gradually narrower towards the top.
Examples: Bolivar TX, Cape Hatteras and Bodie Island NC, Morris Island SC, Cape Florida Fl

A Crib light is a tower and keepers quarter on a man-made island (so to speak).
Examples: Waugoshance MI, Racine Reef, WI (before it was torn down), 4 Mile Crib IL

An In-House light is a beacon on top of a house (I think).
Examples: Old Point Loma WA, Fishing Battery MD

And a Multi-side tower and just that, a tower that has multiple sides (Like if it was octogoanl shaped at the base).
Examples: Sabine Pass LA, Lydia Ann Channel, TX

I'm pretty sure those are the correct definitions. If I'm wrong, please correct me.