Yes - steerer tube is cut depending on the height of the head tube. Many newer forks also use a tapered steerer, so will only work in a frame with tapered head tube (but you may be able to get a conversion headset to mate a tapered head tube with a non-tapered steerer fork).
Assuming the tapered head tube/steerer issue is moot, if it's for the same rider, planning on achieving the same final bar height, adding or removing spacers below your stem as required should sort you out whether or not the head tube height is identical between the bikes. Some forks are also designed for a bike with 'integrated' headset bearings and may look odd on a bike with a skinny head tube, but will still work.
HTH