But aren't there 4 different ways to make a 7th chord? e.g. for C it would be (C E/Eb G B/Bb) so the only way of notating them for me that would make sense is something like "mM7" or "mm7", etc.
Cmaj7 actually means it has maj 3 (note) and maj 7 (note). C, E, G, B...... Cmin7 actually means it has both minor 3rd and minor 7 (notes) in it. so C, Eb, G, Bb...... If you want E natural and Bb in it, that's just called C7. that's just what it's called. the full name for that is C dominant7, but don't be distracted by the word dominant, it's not really dominating anything. it's just called C7. if you want the Eb note but B natural, that's called Cminmaj7, and you probably won't see that very often