Complex, Compound, Complex-Compound, and ;?
A compound sentence uses for, and, nor, but, or, yet, so to give the clauses equal weighting
She didn't like to exercise, but she did at least eat healthy
A complex sentence makes one of the clauses subordinating, providing an emphasis on one of the caluses:
While she didn't like to exercise, she did at least eat healthy.
Another option is sentences that uses a ;, but what is the a proper name for this sentence type, other than enhanced-compound (from what I've found)?
She didn't like to exercise; she had gained weight despite her healthy diet.
You may want to read Wikipedia's discussion of how we classify sentences based on structure. For multi-clause sentences, what matters is whether they're dependent or independent and whether they're coordinated adequately, inadequately or not at all, not whether they're joined with a conjunction, punctuation or both (e.g. a conjunction plus a comma). However, fusion of independent clauses "inadequate" for coordination, with no conjunction and with no or inadequate punctuation, gives a run-on sentence.