Very little practical difference between the two. The longer barrel will theoretically be easier to shoot accurately due to the longer sight radius but when all things are considered, it's a crapshoot. A 4 5/8" that is made right will shoot better than a 5½" with tolerances stacked against it.
Lipsey's is a major distributor for Ruger firearms. Thus, they are able to special order guns made to their specs and do so quite frequently. The 4 5/8" Single Ten is one of their distributor specials and is not a standard Ruger catalog item.