Yes, the TFL approval is for the song, as listed by the band that did it, and the TAFL approval is for the song, as listed by the series it belongs to. Usually people cross-list them (or try to), since it is the same song, after all, but some people know it by the band, others by the anime.
So yes, if one was taken at TAFL, you could apply for the song at TFL if it wasn't listed there, but the fl would need to be about the song and the band... not the song and the anime. ^^;;; Hence, in the links you posted, why the one shows the band, the other shows FMA, on the layout.
I suppose my advice would be that, if an anime song is taken at TAFL, you probably should know something about the song and the band, lest fans of the band get annoyed by a fanlisting focused on the wrong thing, listed at TFL. (Also, the Songs staffer emails me when a fl is obviously trying to be the anime song fl instead of the band song fl.
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