My master's degree in computer science technically says, "Theoretical computer science" as the specialization. I was a mathematics undergrad, and generally enjoy doing proofs, albeit I'm not the best at them.
With that said, I regard TCS as the study of discretized computation at scale. Or, more colloquially, what is the fastest way to do X, N times? This could be sorting, searching, indexing, drawing, tracking, balancing, storing, accessing, saving, reading, writing, whatever. The distinguishing characteristic is complexity analysis in time and space.
As a counterexample, I think cryptographic methods such as AES and RSA are much more pure math / number theory than TCS.