I was recently privileged to take a lesson in classical technique from a local bass teacher. Now I know I am a bass but like anyone else working non-classical repertoire, I routinely sing way up in what is for my voice second and third register.
I was fascinated by the work we did in the session. I haven't revisited Classical technique at all in the years since I began studying SLS and increased my knowledge of voice.
So here's what I got .. The big difference is in the air pressure. The classical voice needs to be loud, and so the pressure is higher, the mouth wider - more of that in a moment - and the chest component is heavier.
The wider mouth - by which I mean chin dropped further - means that all vowels tend more toward ah and there is less textual distinction between vowels.
All of this means a sound that is loud, coloured by the big mouth opening, and does not readily approach 3rd bridge due to its excessive weight over 2nd.