No, those are not remixes, although it's possible the sound emulation could be slightly off. (I remember reading in passing a claim that the vibrato in this game isn't always emulated perfectly, but I also know the Famicom Disk System version has a much less absurd vibrato as well.) It's also possible you're thinking of other tracks from this game--the first is the credits song, and the third is from the final temple...which has different music from the other temples.