In theory generic drugs for humans are the same but they dont always work the same. I had a problem with one generic drug which I now have to get a private prescription for as the generic one made me very ill.
The pharmcsist said that he knew a number of people who had bad reactions to generic drugs and his theory was that the binder that they use to make them, caused the active drug not to work in the same timescale as the branded product and therefore caused side-effects. This would be especially noticeable if its something that you took life long or for 20 years or more.
This may be mainly in drugs which are addictive, which mine is but it has caused me to be very wary of generic drugs. The NHS is very short sighted with generic drugs cos the ones I take are so cheap, there is no reason to stop the branded version being supplied on NHS prescription.
I would worry about generic drugs for animals being sourced from abroad unless a vet thought it was OK.