What is STL?

The language of 3D printing. It describes a surface as a heap of triangles and nothing else - no colour, no texture, no structure - which is exactly as much as a slicer needs. There's an ASCII flavour and a binary one about a fifth the size.

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.