We all tend to think about things as we know them, what we are most familiar with, but in a broader diverse culture there often are other meanings or interpretations (i.e., the soda vs pop vs coke debate). DCL is not promoting any one brand of Coast Guard approved device, therefore their rules use broader generic terminology. I'm sure your daughter will be fine as you seem to be very conscientious about her safety in the water.
Just be aware that the pools onboard are "kid soup" and there is little to no actual "swimming" that can occur. You may find the Mickey pool isn't even waist-deep on your child, so it's mainly sitting and splashing around. As for the family pool, it is deeper but not terribly big, and in my experience so many people are sitting or hanging onto the edge making the center that much less safe because a young one can't get to an edge. My DD won't go in it and she's now 14.
As for beaches, other than
Castaway Cay, you are welcome to use whatever swimming aid you choose. DCL has no control over rules for the local beaches at port stops. The family beach at Castaway Cay is still relatively shallow except at Pelican Plunge, and at that age I would put her in a lifevest if you opt to take her out to the slides.
Enjoy your vacation!