"We are sad."
Translation:Tá brón orainn.
At school I was taught, 'Tá brón orainn,' and it's what I hear native Irish speakers say. Perhaps 'Tá muid brónach,' is a more recent variant - a bit like, 'Tá mé tuirseach,' instead of the more traditional, 'Tá tuirse orm.'
Is this different from "We are sorry?" Have I been incorrect in thinking this was the 'sorry' of apologetic guilt?
It’s not different, and you haven’t been incorrect in your thinking; the literal translation of Tá brón orainn is “Sorrow is on us”.
Note that "brón" is an noun, not an adjective.
You can use "brónach" as an attributive adjective ("scéala brónach" - "sad news"), but it's generally considered "béarlachas" to use it as a predicative adjective.
(Generally emotions/feelings are not used predicatively, but there are some exceptions - "tá mé tuirseach" is used, for example).