Not a dumb question, actually.
They don't have to be the same brand, but naturally manufacturers that make bindings and boots (and boards) do take into account the fit between the boot and binding and board. Burton boots in general go well with Burton bindings, Raiden and Nitro boots, etc.
But I've never ridden a same brand combo of boots and bindings, although if possible, it's certainly worth checking that the boot and binding are comfortable and fit right. In my case, I once had DC boots that went terribly with Ride bindings, causing a pressure point that I just couldn't fix. And my 32 boots are on the bulky side, and the Ride bindings tend to fit poorly in areas, so it's shredded parts of the boots.