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!
"hope that helps"
sort of.
I'm wanting to know if there's a term for a {"chord" that is just a triad with octaves of the of 1, 3, 5}
I already know about terms like "add9" etc; and what they designate.
(Although I wasn't clear that said "qualities" are covered by the larger term of "extension")
I'm asking about a general term/label (such as "scale" "chord" "arpeggio") to apply to this;
for the purposes of my [internal processing] of information and concepts.
It sounds like you are saying a {chord "extension"} = {additional scale degrees; beyond the pure triad}...
So would "expanded" be a good term for a
{"chord" that is just a triad with octaves of the of 1, 3, 5}?
or is there some other that exists; or you suggest?
It seems like "chords" refers to any triad with additional octaves of the 1,3,5
and then triad refers to just the pure 1,3,5
which is kinda stupid to me:
it makes "triads" way more mysterious than they actually are.
triads are just "chords" to me.
and so I want a term that refers to a triad/chord that is just octaves of the core 1,3,5.