The answer is definitely yes- myasthenia is not one disease.

The clinical hallmark of myasthenia is muscle weakness (which may be mild/moderate or severe) affecting any voluntary muscle, and becomes (slightly/significantly/extremely) worse with repeat use of this muscle or muscle group.

So, any thing that will lead to increased fatiguability of the muscles upon repeat use can cause myasthenia. It can be an abnormal gene, an antibody related to each and any one of the proteins that are involved in the process of muscle contraction, as long as it does not lead to fixed weakness of the muscle. (in such a case it will be myopathy and not myasthenia).

probably in most patients it is due to antibodies directed at the acetyl-choline receptor. but, it can also be caused by antibodies directed at MuSk (which is a different illness, in the pattern of involvement, response to treatment, prognosis etc). and possibly other proteins (ryanodine, titin etc.)

It may also be due to a genetic abnormality. and in fact a recent study in Norway found that about 1/70 patients who were considered to have seronegative MG, and were treated accordingly (immunosupression, thymectomy etc) were found to have a relatively common mutation in the Rapsyn gene, and not (as previously thought by their treating physicians) refractory autoimmune myasthenia.
There can also be mutations in DOK7 (again a totally different disease), in MuSK (which may resemble autoimmune MuSK MG), and other proteins.

From my experience-most neurologists are very familiar with classical seropositive AchR MG. some are also aware of the clinical manifestations, results of tests and response to treatment of MuSK. Very few know or are ready to agree that there may be other possible antibodies causing autoimmune MG. and about a similar number show any significant interest or understanding of CMS.

I am personally not aware of any association between MG and CMT.