Personally, I think that the main difference is that aeronautical engineering doesn't deal with rockets and spacecraft, whilst aerospace engineering does. I have colleagues on the other hand who thing that aeronautical engineering is only about the whole aeroplane, and aerospace encompasses structures, fluid mechanics, etc. which he doesn't think is included in aeronautical engineering.
Well I'm no scientific lexicographer but... no hang on, I
am a scientific lexicographer...
I agree with you. I think it's well established that aeronautical engineering includes structures and fluid mechanics. If I wanted to distinguish "whole aeroplane" stuff, I'd use the term
flight mechanics.
FWIW Wikipedia divides Aerospace Engineering into Aeronautical Engineering and Astronautical Engineering on the basis that "the former deals with craft that stay within Earth's atmosphere, and the latter deals with craft that operate outside of Earth's atmosphere". I think that's a useful division.