Is getting hives from nsaids the same as having samters triad? Is one more serious than the other? Are skin-only reactions likely to stay that way?

No. Santeros triad is related to aspirin, asthma and nasal polyps. A rash with NSAID's is a sign of an allergic reaction. It could become worse and even life threatening. You should not continue to take a mecication which is causing a rash unless your doctor specifically tells you it is not an allergy and OK to take.