Red team, black team

The students in a particular class are playing a game. The students are splitted in two teams: Team Red and Team Black. Students in Team Red always tell the truth, students in Team Black always lie.

Anna, Daniel and Claire are three students in the class. The teacher asks Anna: “What team are you?” Anna mumbles something, so the teacher then asks Daniel: “What did Anna say?” Daniel says: “Anna said she is Team Red.” Claire then says: “Anna said she is Team Black.”

What teams are Daniel and Claire in?