Well, I'm not sure what you're asking really, North. If by "distinction" you mean "bands doing something new/distinct from what anyone else is doing", I think there's so few of those anywhere in any case that it's little surprise there aren't terribly many from countries with a) as tiny a population and b) very few large cities than England or America. However, if you're merely sticking to popular music, your frame of reference is probably unfairly specific - much of the traditional music and folk music of the UK which has gone on to influence many later bands is Scottish in origin, Jimmy Shand, James Scott Skinner, Jeannie Robertson etc., and likewise Wales has many traditions (mining bands, singing choruses) that are fairly unique compared to much of the musical landscape. It is worthy of note that these musicians and the traditions that influenced their work went on to form major parts of the musical landscape for the American folk revivalists (such as Pete Seeger, Dylan etc.) and even (reputedly) blues music, which have in turn gone on to spawn basically all of the popular music canon post-1950.
If you're meaning "distinction" in terms of modern bands that have enjoyed much success, then I'd say both Scotland and Wales have produced a lot of bands that compete ably with their English counterparts (especially considering the two countries have a combined population similar to that of London) in terms of both popularity and critical aclaim. Although you may not personally like them or consider that they have any merit, groups and artists such as The Associates, Annie Lennox (cf Eurythmics, one of our best pop music singers of the last 30-odd years in my view), Kirsty MacColl (always a quality artist in my view), prog-rock nobs like Marillion (OK maybe only one good song, but big in their time), Alex Harvey, Nazareth, and then modern bands that have used more folksy-rootsy influences like Deacon Blue and The Proclaimers have come from Scotland. Add in more recent revivalist bands like Franz Ferdinand etc, crappy pop bands like Simple Minds, and this is just off the top of my head - even if you may not like them there is no denying that they've had plenty of commercial and/or critical success over the years. In terms of more original or alternative groups, it's important to note that, being geogrpahically divorced from the London scene and the music industry in the North of England (around Manchester/Liverpool mainly) it's harder for less well known or commercially sounding scottish groups and musical movements to be embraced by music companies, trend-makers and labels. Groups like Sons and Daughters, Arab Strap etc etc over the last few years show there's a thriving "independent" music scene in scotland that isn't necessarily tearing up the top 40.
Equally, Wales has produced a variety of acts over the years both critically and commercially successful, especially impressive when you consider the fact that it's such a small part of Britain. If we're talking pop/rock bands, the last 15 years has produced a number (Manics, Stereophonics, The Alarm, Gorky's Zygotic Mynci, Super Furry Animals, Catatonia) which have had major chart success, and though I would agree that none of these (with the exception of The Super Furry Animals) have broken much new ground or been markedly "Distinctive", they have all been critically acclaimed at one time or another and produced a variety of decent music. Wales is also the home/birthplace of one of the UK's greatest ever pop/rock musicians, and a huge influence on the course of popular music through his part as arguably the prime musical drive of the Velvet Underground, John Cale (who has gone on to produce consistently good stuff for the last 4 decades or so), who by any stretch of the imagination is surely worthy of merit.
More experimental and groundbreaking groups from Wales have included Datblygu and (in a more commercial vain) the Super Furries and Lostprophets. More recently Goldie Lookin' Chain have shown there's still room for joke acts in popular music and have been probably the most successful rap parody act I can think of, though whether you find their stuff funny or not (I think it's very hit and miss!) is probably a personal thing, though the idea of a bunch of white teenagers from a defunct mining town wearing chains and baseball caps and rapping in welsh accents is pretty odd to begin with.
Undoubtedly the biggest influences from Scotland and Wales in popular music would be from more traditional sources, although both countries have produced more than their fair share of commercial and critical successes in the pop music world, and some acts that I've mentioned have undoubtedly been both influential and responsible for what you surely must agree has been some "good" music, however you slice it. To expect Scotland and Wales to have produced as many distinctive and meritous artists as England (with it's larger population, larger cities, and centralisation of the British and even European music recording industry, greater powers of publicity AND all the major music publications, TV shows and most of the more well-known critical outlets in the UK) is probably unfair.
As far as I can tell you're really asking something pretty synonymous with "are there any bands from Scotland or Wales that I like?" in which case it's pretty hard to disagree

.... But however you define "merit" or "distinction" I think you're being a little unfair.