There seems to be some misunderstanding between key and range.
It is quite conceivable to have two completely different songs, one in key C the other in key F, with exactly the same range.Not only in the number of tones but also in which notes are highest and lowest.
The range of any piece is the difference between the highest and lowest notes in that piece. For one voice or one instrument, a range of an octave and a half would be reasonable - a lot of pieces have smaller range, some larger.
So, moving a piece out of key by half an octave - up or down - shouldn't phase instruments, although singers with limited ranges may baulk.
The range of a piece is often not a lot to do with the tonic note - it may start or end on it, but whether the rest of the notes are mostly or all above or below that note will depend on how it was written.
Bearing all this in mind, a particular song may be too high or too low for a particular singer, so a different key needs to be used. So that the song's range and that of the singer match.
However, if you are considering one song in particular, then moving its key from C to F could have two distinctly different results.A singer may then not be able to reach the high notes, so would sing it down, compared with another singer who was happier singing it up an octave higher. Which is maybe where your question emantes from. Not sure.
Your last paragraph is also difficult to answer. A sequence of, say, I vi IV V - quite common - will work exactly the same in any of the 12 keys. in key C it's C Am F G, in key F it's F Dm B♭ C, and in 12tet there will be no difference, except that one will sound higher (or lower!) in key F than it does in key C.
I just hope I interpreted the question accurately! Voicings are really a different issue.