Question. Is there really any difference between the 2 types of a "returner"?
Why not just have washington be the returner for both?
We've seen plenty of guys return both punts and kickoffs before, including your example of L.Washington.
Danny Amendola had both return duties in his first 2 seasons in the NFL, and he actually led the league in KO return yardage that year to boot.
Julian Edelman has also done both, but has been much more efficient on PR's.
To answer your question though, KO returns are more dangerous and violent, with a higher tendency for injury due to the speed of the play itself. One needs to have good straightline speed, good vision, and an initial good burst right from the get-go for kickoff returns. The kickoff return is a much faster play, and actually is the fastest play possibly in all of sports.
Punt returns--are a much slower play in general, where the chance of injury is not nearly as high. To be a successful PR man, one must be shifty (like Edelman), with the ability to be able to juke and make guys miss. It's more likened to a YAC kind of play, as opposed to KO returns, which are much more about blazing speed, initial burst etc. This is why we see Edelman/Welker excel at the bubble screen kind of plays, where they can just grab the ball and make a couple of moves..and BAM.
Of course some of these traits are going to go hand in hand with each other at times, but that is the general breakdown of the differences. Generally one player will be chosen to be the "top" example of their duty, such as Washington on KR and Edelman on PR; but if an injury occurs either player can handle either duty.