'... two objects made from the same factory' cannot be one and the same object. Whatever their sameness in the sense that each object has all and only qualities exactly similar to the other's, they are numerically distinct.
'Identical' is an ambiguous term. It can connnote exact similarity as when each object has all and only qualities exactly similar to another's - or it can mean that X and Y as identical are one and the same object as in Frege's example of the Morning Star and the Evening Star's being identical because they are one and the same object differently referred to, i.e. the planet Venus.
This is not confined in its application to mathematical objects. 'The same ...' is incomplete. The same what ? Two automobiles can be of the same model, where there is nothing mathematical about a model (in this sense). Three people can belong to the same family - another non-mathematical object. Mathematics enters necessarily at one point only: countability is implicit in the concept of sameness. Am I the same person that I was yesterday? Yes, I am one and the same person at two different times. If I am in New York and move to LA, have I been in two locations in one and the same country? Yes, of course, the USA.
'Equality' can mean 'equality in numerical value' as in your apples example but when I say that two models of automobile are of equal utility for your purposes - one's as good, as functional, as the other it's hard to see what strict metric I could use to justify my claim. I just mean, one's as reliable as the other, one's as easy to get serviced or repaired as the other, they equally enhance your image, &c.