The only thing needed to be the same is the active ingredient. A pill is more than that, it is fillers, coloring and heaploads of other stuff. It is not uncommon there are 8-10 different substances in a pill.

On average, generic meds have more extra substances.

Some substances might be the same as the original med, some might be different.

There is a med which I can take the generic of but not the brand name. So it can work in that direction as well. It can be tricky to find out what substance is the troublesome one, but comparing lists of what is in the pills can help.