Tenor, Sorprano and Alto are different ranges of notes. I'm not sure the exact values, but Tenor is the lowest of these three, hitting inbetween bass notes and melody notes. Sorprano is mostly melody notes, and Alto is high pitch melody notes. There is actually a fourth-Bass, which hits the low bass notes.
Anyway, so your ocarina is relatively low pitched, though can probably still hit some melodic notes.
However, its pitched in the key of F, so it'll be higher than one pitched in C.
Basically the four groups are ranges at different levels of the spectrum of notes from melody to bass. Having an instrument at a different key simply shifts those ranges higher or lower depending on the note.
Hope this helps!
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