What is OFF?

Object File Format, and about as plain as a mesh can get: a count of vertices and faces, then the vertices and faces. It comes out of academic geometry work, where nobody wanted to parse anything more complicated to test an algorithm.

What is PLY?

The Stanford format, built for scanned data. Its distinguishing feature is per-vertex attributes: colour, normals, confidence values, whatever the scanner recorded. Research and photogrammetry tools default to it for exactly that reason.