The point is, the sauce made with browned butter is called black butter, that is its name - I doubt whether it is used under any other name. If it is I've never heard it, in fact I don't think I've ever had it but it sounds delicious. If we had eaten it in our childhood, we would have called it that without any thought of pretentiousness - unlike puree de pommes, which we already know as mashed potatoes.
Pan-fried is to distinguish it from deep-fried, which is not the same. If a menu said sauteed instead, perhaps there wouldn't be the "pretentious" reaction to it. However, sauteed is French, pan-fried is English. Which is more "gourmet" (or "fine dining" if you prefer)?
When I said "Pass the gravy" to my amateur chef son-in-law (the one with a smoker thing the size of the boiler on the Queen Mary in his back garden) he assured me that a jus is NOT gravy, that gravy is made with thickening and extra water, but a jus is just meat juice. Right enough, it is usually thinner and you don't get as much of it. Tastes good though.