This tutorial covers the basics of chord theory.  It will answer most of your questions.

https://www.guitartricks.com/tutorial/148/

Directly responding.

"like would a em7 {1, 5, m3, m7} be an "expanded triad"?" "are the words expanded and extended used in relation to triads or chords?"

Yes, extended harmony chords is the commonly used term.  Some musicians reserve the term for chord tones beyond the 7th, starting with the 9th, including the 11th, 13th.  I prefer to call anything beyond 1-3-5 as extended.

Extended Harmony Chords Series 1
https://www.guitartricks.com/tutorial.php/1166/

"does the term differ... depending on if it's just octaves of the 1, m3/3, 5... or other scale degrees added or substituted?

Chords with other scale degrees are labelled by those degrees as well as with various chord quality terms:  add 9 , sus 4, etc.

Hope that helps!