I don't own any Kates but I have Iriza's.
Iriza pumps do have a gap on the size that gives the foot more room, as opposed to a Kate that completely closes around the foot.
Iriza nude patent size 37, 100mm
Iriza black nappa size 37.5, 85mm
(My true size for most heels are 37.5)
Personally I think the 37.5 in nappa are a tad too big. It's not slipping out when I walk but I do notice the difference. If I buy another pair in nappa leather I would go for 37.
However, even each pair of heels varies in size slightly. I recently tried on a pair of 100mm, black patent Iriza's in 37.5 and I found it to be quite snug even though I own a pair in a 37.
If you can return it easily, you can get them to try on and make sure they fit.
Otherwise, for any pair of heels, I'd rather try on in stores and buy the pair that fits my feet the best.