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Sliding away from the more snide definitions...
Dark RP - I think people usually mean for this to describe plots and elements that one would find in the Dark Fantasy genre. Elric, The Black Company, Dragon Age, Berserk, stuff like that. Expect a bit of forefront of violence. Expect moral shades of grey. Expect protagonists rather than heroes. This can get tied up in cliche as much as anything, most typically it gets wrapped in a "gothy" package, but it is a bit of a misrepresentation of the style. While gothy elements can exist, there are plenty of places to go without everyone being dressed in black. A Song of Ice and Fire/Game of Thrones is a prime example of Dark Fantasy. Oh yeah, last defining feature, expect bad guys to possibly win.
Mature RP - I tend to think of this tag dealing with more mature subject matter. Sex and sexuality are certainly there, but the net also catches things like racism, class issues, and religion. The general intent is to approach and explore said issues and not shy away from the more controversial bits. Each subject handled with maturity and open minds. This gets a bit strange because this is really more of a subject matter tag than a genre tag. So there is a lot of bleed over between the two.
So, to me, one is a genre tag the other is a subject tag. Wheee!
Hope this has been helpful, yar.
Dark RP - I think people usually mean for this to describe plots and elements that one would find in the Dark Fantasy genre. Elric, The Black Company, Dragon Age, Berserk, stuff like that. Expect a bit of forefront of violence. Expect moral shades of grey. Expect protagonists rather than heroes. This can get tied up in cliche as much as anything, most typically it gets wrapped in a "gothy" package, but it is a bit of a misrepresentation of the style. While gothy elements can exist, there are plenty of places to go without everyone being dressed in black. A Song of Ice and Fire/Game of Thrones is a prime example of Dark Fantasy. Oh yeah, last defining feature, expect bad guys to possibly win.
Mature RP - I tend to think of this tag dealing with more mature subject matter. Sex and sexuality are certainly there, but the net also catches things like racism, class issues, and religion. The general intent is to approach and explore said issues and not shy away from the more controversial bits. Each subject handled with maturity and open minds. This gets a bit strange because this is really more of a subject matter tag than a genre tag. So there is a lot of bleed over between the two.
So, to me, one is a genre tag the other is a subject tag. Wheee!

Hope this has been helpful, yar.