While the “-tte” indicates a diminutive, cocottes aren’t particularly small. I wrote “a kind of” because I associate particular materials with them, including the enamel, which I don’t necessarily with what is called a casserole in English (which in turn is different from what is called a “casserole” in French, which is more a sauce pan). Maybe someone else has better knowledge about those cookware terms.
It seems cocotte = English 'casserole'; casserole = saucepan.
The enamel vs. cast iron interior of a cocotte IME in the UK is not significant, but in the US going by Wikipedia anyway enamel = French oven; pas d'enamel = Dutch oven.
...I suppose we've no hope of agreeing on all this if we can't even have a 'cup' be the same size! (Or convince Americans that they shouldn't be (and in many cases would find it easier if they weren't) using volumetric measures for everything anyway, for that matter.)