I reckon you're correct, Christine. :clap:
I don't have either of those items in my collection (nor have I ever had) so I can't speak from first hand experience, as I can't examine them. I've studied the photos in Baxendale's book - she shows both the items. The rose bowl (cupped in shape) has long been known as Kokomo. In fact I think it was once thought to be American (hence the name). The flared out bowl was named Star and Studs by Mrs Quintin Baxendale! She shows both items in her book.
Possibly best to continue to refer to them as separate names for now, with Kokomo referrring to the rose bowl only. But wise to cross reference them for clarity and full information. (Oddly, there is precendence for different pattern names in Carnival Glass).