Originally, DUB referred to the fundamental elements of Reggae music, as when artists would release versions of tracks simply stripped down to
drums and bass. This evolved into some of the first things we'd think of now as "remixes" as the studio engineers began to play with these stripped down tracks--using lots of echo and reverb to change the rhythms around and bringing in (and out) different instruments minimalistically. Eventually, I think, the terms 'dub' and 'remix' became more or less interchangeable.
Usually remixes are done under the aegis and auspices of the artist who wrote the piece in question. As to the broader question about sampling and remixing and copyright issues,
Negativeland's Intellectual Property Issues Page is still a great and fairly timely collection of articles from many different, mostly fairly radical points of view concerning such concepts. (ie: 'The Art of Noise's Futurist Manifesto,' 'Artists Against Intellectual Property,' 'Copyright Law is Wrong,' 'Musicians Against the Copyrighting of Samples,' 'Negativland's Tenets of Free Appropriation,' and much more)