Have a look at Complete Vocal Technique.

https://completevocalinstitute.com/complete-vocal-technique/

Their work includes pedagogical research to develop a consistent terminology which abandons lots of outdated and confusing terms such as you mention. No more ambiguous words like "project" or "space" or "support".

Their research also includes using endosciopic cameras to directly observe the vocal tracts of professional singers.

I've not actually trained with them, I just like their research and approach.