(Ok, I take that back, In-n-Out Burger is more overrated than both.)
(I say jewish rather than kosher, because many of the best bagel places don't qualify as kosher. At Vancouver's best bagel place (siegels) you can get cheese on your Montreal smoked meat bagel.)
I've never heard of "Jewish bagel".
Montreal bagels are "Jewish", and are the opposite of New York bagels.
The mass-produced-in-a-factory-with-lots-of-preservatives bagels (e.g. Lenders) are very different, but also obviously made with yeast, and they don't really resemble fluffy white bread IMO.
When I go to my local grocery store in the northeastern US (the chain is in fact owned by a Jewish family), both kinds are available, the one in the bakery area and the other on the shelves with rolls.
Talking about these as though the dividing line was Jewishness or the use of yeast strikes me as both weird and incorrect.