They are very different things. One is based on ignorance. The other is based on outright falsehoods. To gain the benefits of being an Indian, You. Have. To. Have. Paperwork. I guess this isn’t the case with affirmative action (but Lizzy Warren is a woman, and I reckon that counted more if it mattered at all) but if you want concrete benefits, you have to prove it.
Stolen valor, on the other hand, is someone — for whatever fucked up pathetic reasons — is going around deliberately misrepresenting what they have done. Showing up at funerals of dead Americans wearing silver stars.
Very different things.