Todd is correct. However, I feel like being a little more loquacious.

Black Watch in modern colors is the same as Campbell in modern colors. Black Watch in ancient colors is the same as Campbell in ancient colors. Black Watch in weathered colors is the same as Campbell in weathered colors. And so on. Different mills may have slight—or even quite noticeable—differences in thread count, but it's all essentially the same tartan.

Changing the shade of the tartan does not ordinarily change the tartan itself. The Graham of Menteith tartan in ancient colors and the Graham of Menteith tartan in modern colors are both the Graham of Menteith tartan. It just so happens that the Black Watch/Campbell tartan does double duty. Well, it does more than double duty, but let's leave it at that for now. The Black Watch has worn their tartan in modern colors since modern colors (i.e., chemical dyes) were invented in the 19th century. The Campbells wore the same. When ancient colors (i.e., chemical dyes attempting to mimic faded vegetable dyes) came into fashion in the 20th century, naturally some Campbells began wearing their tartan in those colors. This had the added practical benefit of distinguishing them as Campbells, since the Black Watch never wore kilts in ancient colors.

Not surprisingly, this has caught on, to the point that it is reasonably safe to assume that someone wearing the tartan in ancient colors identifies with Clan Campbell, while someone wearing the tartan in modern colors is just wearing the Black Watch tartan, which is often regarded as a universal tartan that anyone is entitled to wear. In that sense, you could say the shade of the tartan has meaning. However, it's still always possible that the fellow wearing the modern colors is a Campbell, while the fellow wearing the ancient colors just prefers to wear the popular universal tartan in the ancient, rather than modern colors.