While a little confusing for those who are not mathematically inclined (like me!), Bart is absolutely correct.:)
On the surface (no pun intended), it is easy to think that 2k has twice as many particles as a 1k, and 4k twice as much as 2k. But it is the math that Bart explained which answers another question on what Glen identifies as restore vs. sharpening/bevel setting earlier on the thread
here or just scroll up. (Are you following?:confused:)
At the 4K level, the particle sizes are too small and too shallow to effectively create a new bevel. The 4K can, however, remove just the thinnest layer to expose a "refreshed" layer of the bevel, like taking one layer of skin off an onion. You will not get to the core of the onion on a 4K in this lifetime - you'll most likely get to the core of the 4K if you try, though!
So to expand on Glen's answer, an already well defined bevel that is simply dull and needs to be
honed can benefit from starting a 4K.
If the 4K doesn't seem to give results, from an uneven or a rounded bevel from stropping, for example, the one would require a coarser stone to reshape, or
reset the bevel (i.e. 1k, 2k) - this should be relatively fast since the existing bevel is basically in place (in theory), and it is just a matter of peeling down the rogue layers of the skin of the onion so that an even layer of skin is exposed.
Restoration is removing whole layers of metal on the blade to get rid of chips, rust, and/or pitting and requires a lot of effort and a maybe even a coarser stone such as a #220.
:D