I suppose there might not be an exact deffinition of a crate engine, but I've usually seen it used to mean an engine that is more or less ready to un-box and fit in a car, and that has most, if not always, all, bolt on ancilaries fitted.
ie the Kitspare one has:
- Throttle body - Engine loom - Injectors - Fuel rail - Inlet and Exhaust manifolds - Leads and plugs - Coil pack - Water pump - Clutch - Flywheel - Thermostat housing - Oil filter - Sump
You have different terms for different "amounts" of "engine" that you buy, so you can also buy crate engines, half engines and short engines.
Half would IIRC be just the basic block, crank, rods and pistons.
Short, again, IIRC, would be the more or less complete lower lower half of the engine, ie an almost complet unit, but twith no head or inlet manifold/carbs/throttle body or anything else attached to the head.
I guess you don't see all the terms used so much now as in the days when cars needed engine replacements or major overhauls quite so much.
Zetec engined were built in big numbers and loads of spares would have been made to service the spares requirements up to and after the end of the original cars lives. After that, they get steadily less valuable. (Except where for some reason a particular motor becomes sought after and artificially keeps value high)