I think the question was whether you would get 3.5" or 3.75" finished HST from a square that's cut at 3 7/8" or 4". The answer is - neither! You will get a 3" finished block. But you will trim your HST to 3.5", which is what I think you meant.
For the method of adding 1" (or 7/8" for those who still have their eyesight and don't like to trim - not me!) you add that 1" to the desired finished size of your block. So if you want to end up with 3.5" finished blocks, you need to cut your HST squares at 4.5". If your directions say to cut 3 7/8" (and you're going to cut at 4" instead) you will trim your HST to 3.5" as you say, but your FINISHED block size will be 3".
Confusing, huh? 4", 3 7/8", 3.5", and 3" all in one little HST.