I think "kit" has a particular inflection in Britain, as "a nice piece of kit." "Video Gear" in the States, to me anyway, is a generic term for anything relating to video impedimentia, whereas a "Kit" implies a complete set of something, usually in the context of a turn-key purchase. I have all kinds of video gear --- mikes, lenses, lights --- but I bought a lighting "kit" which included three heads, stands, cables, lamps, case, etc, and all the necessary pieces to work with. That's the distinction as I understand it....

understood.

in the uk the coordinator would ask the shooter/director for their kit list (all the bits and pieces inc camera, lights required) in US would that be called gear list?

Most likely, although there's no hard-and-fast rules, "kit list" would be entirely understandable. Language -- at least on this side of the pond -- is pretty flexible...