The term minor has more than one meaning as it relates to keys/scales versus intervals. You cannot simply look at the distance between the notes in a given scale to determine the name of the interval. Allow me to explain.
C D E F G A B C is a C-major scale
C D Eb F G Ab Bb C is a C-minor scale
So, you are correct that C-major and C-minor have some intervals in common, and that C to D is common to both scales. C to D is a major second (or a whole step) regardless of what key one is in.
C to F is a perfect fourth in both keys – it is not a major fourth in C and a minor fourth in C minor. The interval is always a perfect fourth. Similarly, C to Bb is not a minor seventh; it is a dominant seventh.
To make your life easier, let's look at all ascending intervals from C to C.
C to C# (or Db) is a minor second. As Glenn B. noted in an earlier reply, this is also called a half-step.
C to D is a major second or a whole step.
C to Eb is a minor third.
C to E is a major third.
C to F is a perfect fourth
C to F# is an augmented fourth; C to Gb is a diminished fifth
C to G is a perfect fifth
C to Ab is minor sixth; C to G# is an augmented fifth
C to A is a major sixth
C to Bb is a dominant seventh; C to A# is an augmented sixth (very rare)
C to B is a major seventh
C up to C is a perfect octave
I hope this helps.