After reviewing some recorded footage I have found that in the single frame in which you land, all horizontal movement is lost. This is any landing, not just after you jump.

From what I can tell, jumping (including ink jumps) has the same horizontal movement as running. So it may be preferable to jump at times rather than simply running off things.

For example, the two story house followed by slightly raised ground in the starting village. If you start at the top, you could simply run off it without jumping and then jump up to the raised ground (3 landings). Or you could jump and ink over to the raised ground (1 landing). In this scenario, jumping saves 0.06 seconds.

It's not much, but with all the other unnecessary jumps and other landings we're probably still making, it should add up.