having bred animals over a lomg period also buying and selling in that time, i have seen a lot of descriptions fitting pairs of any animal.
a pair to me are a male and female, ie: shoes left and right etc
with birds a bonded pair are a male and female who get on together and possibly mate
a breeding pair are a male and female who raise young
you usually pay more for these as there is a chance of getting some outlay costs back
usually if citing a pair of fish, birds etc as a breeding pair the description will be added to by, lays fertile eggs but male breaks or eats them, eggs must be taken off parents, babies must be hand reared etc