I have always thought of rebloom, as one scape finishes blooming and another scape then emerges.
And recurrent as one scape is blooming and another scape emerges while scape number 1 is still blooming.
A purchased a few of Karol Emmerich's for their recurrent bloom since here north of Boston there is not sufficient time for rebloom to occur. (Needs a longer rest period)
I once compared notes with Gail Korn on our growing conditions, the same plants and her many reblooms and my hardly any reblooms. We concluded that her growing season AND her number of heat days (over 90) were much higher than mine.
I live north of Boston and Gail lives in Nebraska. I am zone 6 and she is zone 5 (now maybe 4?)