As the sibling said, even if you consider cosmology a subfield of GR (which it is only to a small degree), not all relativists will be cosmologists. But you wan

As the sibling said, even if you consider cosmology a subfield of GR (which it is only to a small degree), not all relativists will be cosmologists. But you wanted me to expand on this a bit, so here you go: Cosmology is concerned with the cosmos as whole, i.e. the largest scales of the universe. GR looks at large scales, but not necessarily the largest ones. (A typical black hole is much smaller than a galaxy.) But this is not the only difference between the fields: General Relativity is just one tool inside a cosmologist's toolbox. Most of them also need quantum field theory, statistics and image processing in their daily work. The reason is that, while Relativity by itself is usually only concerned with theory, and mathematical GR even more so, cosmologists have to match their theories to actual observations. They are interested in the history of the universe and in the large-scale (average) behavior of what you can see on the sky. Meanwhile, mathematical GR is mostly a mathematical endeavor. People in that field tend to be mathematicians, with a background either in analysis / PDE theory or in geometry or both (geometric analysis). They are interested in physics-inspired questions but not exclusively so.