What is OBJ?
Wavefront OBJ is plain text, thirty-five years old, and readable by every 3D application in existence. Vertices, faces, texture coordinates and named groups, with materials kept in a separate .mtl file alongside - which is the part that most often goes missing when a model is shared.
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.