This is an interesting categorization.

Mine would be:

Alpha Dominant

Dominant

Service Top

Fetishist

In short:

I'd make a separate category for the Alpha types versus "standard" Dominant people. I think we, as one who identifies as such, have a particularly strong, Dominant personality.

"Standard", for lack of a better word right now, Dominants likely have Dominant personalities but might tend to be more yielding or lack some of the personality characteristics that Alpha types have.

In my opinion, based on several conversations with people and my own observations, that several people who identify as a Domme are actually service tops. How much is "several"? I don't know. I just think it's probably as common as people who identify as submissive and are not but are actually "just" a bottom.

Then we have Fetishists. I think by and large FinDommes are really money fetishists. It's all about the cash. There is no interest in the craft of power dynamics, as we understand them in BDSM, and the psychology of eroticism. It's just "How hot is it that I ask for $20 for pizza and this dude gave it to me!"