I like the taxonomy of French and Raven's bases of power:

https://en.wikipedia.org/wiki/French_and_Raven's_bases_of_po...

In this framework, I tend to associate charisma with referent power, which deals with power through identification, admiration, and respect. This could be Bill Clinton's ability to feel your pain or Donald Trump's ability to tap into a sense of nationalism.

To answer your question more directly, the answer is no. Referent power is one kind of power. There are many others. Certainly, this is all debatable and not cut and dried, but I do like the bases of power linked to above as a way to create a vocabulary to talk about it.

Both are possible. You don't need power to be charismatic and you can learn to be more charismatic, but if you display charisma without power then you will be attacked frequently by those who have more of the latter.