This is the normal situation on a guitar tuned to Standard Tuning (EADGBe). The A string is tuned one fourth above the E string. And this interval is just 4 semitones or frets away.
Going from the G string to the B string there are only 3 semitones in the middle. This is because B is a Major third above G. It is a little weird and guitar players all have to get used to it at some point (or tune differently).
So, except for the extreme bottom and top of the range, there are usually several string+fret combinations which will produce the same note. And to play a chromatic scale, you could do it in several different ways
$6.0 1 2 3 4 $5.0 1 2 3 4 $4.0 1 2 3 4 $3.0 1 2 3 $2.0 1 2 3 4 $1.0 1 2 3 4 5 6 7 8 9 10 11 12
$6.0 1 2 3 4 5 6 7 8 9 $4.0 1 2 3 4 5 6 7 8 $2.0 1 2 3 4 5 6 7 8 9 $1.5 6 7 8 9 10 11 12
$6.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 $1.0 1 2 3 4 5 6 7 8 9 10 11 12
And one more, which probably how I would choose to do it if I wanted the visual effect of moving all the way across the fretboard:
$6.0 1 2 3 4 $5.0 $6.6 7 8 9 $4.0 $5.6 7 8 9 $3.0 $5.11 12 13 14 $4.10 11 12 13 $3.9 10 11 12 $2.9 10 11 12 13 14 15 16 17