You are absolutely right. I’ve been collecting Vai guitars for so long I think of them all as JEM’sLovely guitar!!!
Although... let me pick some nits here...
I thought all JEM:s were 6-stringers(with the thru-body monkey grip handle)...
... whereas the Steve Vai -designed 7-string(and grip-less) series was called Universe.
That thing sure looks like a Universe to me... CS or not.
On a semi-related note... the UV7BK was the first 7-string I ever touched.
Never owned one though.
You can however get a 7 string JEM. Monkey grip, wizard neck and all. This one was my daily driver for a number of years.