There is no difference in meaning.
However, ceea ce is perceived as being more formal, while ce is more colloquial and also more widely used.
Keep in mind that you cannot use ceea ce when asking a question (it only works as a compound relative pronoun, not as an interrogative one). Use only ce to ask a question.
Is there a reason for the feminin form "ceea"? Could it also be "cela ce"?
It's always "ceea ce". Actually, besides this fixed compound pronoun, you never come across the forms cela, ceea, ceia and celea in standard Romanian. They may only be used regionally.
As for why the feminine, I'm not sure, but as a rule of thumb, we tend to use the feminine of certain pronouns when they have a general meaning:
Ce-i aia? = What's that?
Asta mă întristează. = This makes me sad.