This is largely copied from one of my very recent comments for which I did a bit of thinking.

In the US, we call the entire box the stove, the surface the range, and the inside the oven (afaik anyway).

Colloquially, we call the surface (i.e. the range) the stove (or stovetop).

So, when you say you're going to buy a stove, people understand you are buying a box that heats things up both on the inside and on the top. But you also wouldn't say "I'll put the cookies in the stove", although you could say "I'll put the pan on the stove" to mean "I'll put the pan on the stovetop", which is synonymous with "I'll put the pan on the range", although you'll get funny looks for that.

I guess it makes sense, because "oven" only takes "in" and "out": you can only put cookies in the oven or take them out. However, "stove", in its meaning as the entire box, can technically take "in", "out", "on", and "off". So, it makes sense to relegate "in" and "out" exclusively to "oven" (since that's its "specialized purpose") leaving "on" and "off" for "stove", which makes it absorb much of the function of "range".

Does this make sense? Does anyone think this might be an adequate explanation?