More importantly, "Permanent skill" has a specific meaning in a Lemmings context, and those are the skills usually considered to fall under it. It's been debated exactly which category Cloner should fall under, but I don't believe permanent has ever been proposed - some proposals have put it in the same category as Walker and Shimmier, while others consider it to defy categorization and be in its own category by itself. I don't recall ever specifically seeing it included with the permanents.
The unambiguous categorizations (current or very-likely-future NL skills only) are:
Movement skill - Walker, Shimmier, Jumper
Permanent skill - Climber, Swimmer, Floater, Glider, Disarmer
Constructive skill - Platformer, Builder, Stacker
Destructive skill - Basher, Fencer, Miner, Digger
Some people would put Bomber and Stoner under destructive / constructive respectively, though it's more common to group the two together under "Fatal skills" or some other term like that. Blocker is sometimes included with these, sometimes included with Movement skills, and sometimes considered unique much like Cloner can be. It has been recognized that the Blocker shares traits with the permanent skills to some extent, though I don't think I've actually seen it considered to be one - such recognition is usually been used more to say "the blocker should be next to the permanent skills on the skill bar".
Of course, this kind of discussion is of limited importance in terms of actual gameplay, as the skill will do the same thing regardless of what category you consider it to fall under. The only time it's had direct relevance to NL is in discussions of how to order the skills on the panel, but so far the only time such consideration has been applied was in deciding where in the order the Fencer and Shimmier should go - the other 8 skills predate much consideration of such, and have just kept the order they were originally assigned (although this does end up quite strongly reflecting the above anyway).
