Orthogonal set vs. orthogonal basis

When you say orthogonal basis you mean that the set is a basis for the whole given space. Every orthogonal set is a basis for some subset of the space, but not necessarily for the whole space.

The reason for the different terms is the same as the reason for the different terms "linearly independent set" and "basis".

Every linearly independent set is a basis for the subspace it spans. But when working in a larger space "basis" means "maximal linearly independent set" (not just spanning a subspace but spanning the whole thing).

An orthogonal set (without the zero vector) is automatically linearly independent. So we have "orthogonal sets" and then maximal ones are "orthogonal bases".

Note: In the end we're essentially just tacking on the adjective "orthogonal". We don't keep the words "linearly independent" in "orthogonal linearly independent set" because they're redundant.