Is the solution space of a homogeneous linear system the same as the null space? Is the solution space of a homogeneous linear system the same as the null space?
If not how do they differ?
(sorry if this is a really stupid question)

That's pretty much correct, all I would do is to make a slight correction to your mathematical grammar. Given a homogeneous linear system of equations written as a matrix equation $MX=0$, the solution space of the system is the same as the null space of the matrix $M$.
