Many people consider Sonic Colors, or at least it's DS port, to be a spiritual sequel to Sonic Rush Adventure. This is supported by the fact that the DS port uses the same engine and mechanics used in the Sonic Rush series, with the addition of the Wisps, as well as being created by the same developers of the Sonic Rush series. However, when I examined this theory, it seemed quite far-fetched.
The Sonic Rush series revolved around Blaze and her interaction with Sonic and his friends. While Blaze does appear in this game, her role is reduced to that of a supporting character. She has no relevance in the story whatsoever. She is not even playable; Sonic himself is the sole playable character. There was really no excuse not to make her playable; since there was already a model for her from the Sonic Rush games, it should have been extremely easy to put her in the game, if only as an alternative to Sonic. Nothing bad could have come from making her playable. She was simply debased to a supporting role.
Sonic Colors' setting also has no relation to the setting of the Sonic Rush series, being based in Eggman's theme park in space, while the setting of the Sonic Rush always had some relation to Blaze's world. In Sonic Rush, the setting was Sonic's world, but Blaze's world is slowly merging with Sonic's, creating the threat of both worlds' destruction, while the final boss battle takes place in the gap between dimensions. In Sonic Rush Adventure, the entire game is set in Blaze's world. Both games build on the mutual relation between Sonic and Blaze's worlds.
It may just be because I harbor a sort of personal vendetta against Sonic Colors, since it popularized the "Sonic only" trend started with Sonic Unleashed and bastardized the supporting cast, but I feel that the theory that Sonic Colors is a sequel to Sonic Rush Adventure is somewhat outlandish. The two games do not share a setting or even a relation between the settings, and Sonic Colors also debases the Sonic Rush series' deuteragonist which it is built around. The only things the two share is a game engine, play style, and developer.