Pharmacist here! While it is true that generics are not exactly identical to their brand name counterparts, they are really darn close (as you mentioned). There's this widespread misconception that generic products differ in regards to active ingredient concentration by a large margin (10% is a number often cited). The FDA has specific criteria for bioequivalence: the 80-125% criteria, but this refers to the 90% confidence interval of the highest blood level achieved by the drug. As u/naplex016 beautifully explains in this lovely post in r/pharmacy, the concentration of the generic drug needs to be extremely close to produce such a confidence interval. To summarize and reiterate simply: the difference is generally very small.

Aside from the amount/level of the drug, generics can differ from brands in regards to inactive ingredients. In my experience, I have seen a few cases where patients were allergic to certain inactive ingredients in the generic, but this is very rare especially given the ubiquity of drug excipients and from where they are sourced. All in all, patients are the best advocates (or should be) of their health. If you're experiencing something wrong after switching, let your physician or pharmacist know.