The musical interval of an octave can also be referred to as a Perfect Octave, or an eighth. It is fairly obvious that the word means 8 of something, so 8 whats?
It does not mean 8 steps, because it is really 7 steps away...specifically 5 whole steps and 2 half steps. If you are playing chromatically, then the octave is 12 half steps away. So, the 8 does not come from the number of notes you have to play to arrive at the right note, it really means "the 8th" note in a scale in which you count the starting note as "1" and the next note as "2", and so forth.
Have you ever noticed that there are only 7 letters used in the musical alphabet? A-G, right? So, if you start on "A" and think of it as "1", then count up through B, C, D, E, F, and G, then you have to use "A" again to get to "8". It doesn't matter whether you are using a major scale, minor scale, or any other type of scale. As long as you only use each letter once (with any combination of sharps or flats) you will arrive at the same letter that you started with for the 8th note.
This brings up an interesting question: Why is the octave so important that it caused early musicians to base the whole system of music theory on 7 note names? (Remember, 7 note names + 1 repeated note name = 8, or the octave) The answer is complicated, but I will give a somewhat simplified answer.