Piston engines:
"Short" block: the lower half of the engine, from the headgasket down (no head or heads, depending on engine.)
"Long" block: the entire engine, sometimes with manifolds.

Rotary engines:
"Short" block: just the assembled engine.
"Long" block: assembled engine with manifolds.

Long blocks are cheaper because it's just the engine. What one needs to "work" depends on the engine and intended body.