Alright, imagine you have a bunch of lines written down on paper, like a list. Each line has some words on it, and some spaces between those words.
This GREP (?m)^[^\s]+\K\s, is like this:
You go through each line, and when you find the first word on that line, you put a special mark after it.
Then, you look for a space after that special mark.
So basically, you're just picking out the space right after the first word on each line.
Your GREP:
^[^\s]+\K\s, is a bit simpler.
You look at all the words on all the lines together, not one line at a time.
You find the first word in the whole bunch, put a special mark after it, and then look for a space after that mark. So here, you're just finding the space right after the very first word in the whole list.
So the difference is like looking at each line separately for the first one
and looking at all the lines together for the second one
Hope that is clearer