Atque, according to L&S, means
a copulative particle, and also, and besides, and even, and
According to Bennett's New Latin Grammar ch. 6 §"Coordinate Conjunctions", "atque is used before vowels and consonants; ac never before vowels, and seldom before c, g, qu."
L&S continue, saying that atque
indicat[es] a close internal connection between single words or whole clauses; while et designates an external connection of diff. objects with each other
So, it seems these would make sense:
mulier ac mater
(a woman and also a mother ← related)
pater et arbor
(a father and a tree ← unrelated)
Bennett also mentions that -que binds more tightly than atque.
It seems this analogy would hold:
vel : aut :: atque : et
"inclusive disjunction" : "exclusive disjunction" :: "inclusive conjunction" : "exclusive conjunction"
As I mention in my comment here
§C of "sive
" says it's disjunctive.
(Interestingly, L&S also says vel was sometimes used in a "purely disjunctive sense," so there is some evolution in these "or" words.)