We are all, to a certain extent B”T every time we are mekayeim a mitzvah whoch we did not do beforehand in the proper way. But what is generally meant by the term, is not the frum Yid who tries to grow in his Torah and Yiddishkeit, but rather the Yid who was never minimally frum to begin with, or who was OTD, and in both cases, returned to frum observance.
You are correct in the common usage of the term, and I think you answered the OP’s question.
To the best of my knowledge, the original term technically can refer to anyone who has done teshuva (which involves regret, besides proper observance) from even one aveira.