the rating you get after every game is dependant on the mode. so if you win in rapid then you gain elo in rapid, if you win in daily chess then you gain elo in daily chess.
What's the Difference Between the Types of Ratings?

the rating you get after every game is dependant on the mode. so if you win in rapid then you gain elo in rapid, if you win in daily chess then you gain elo in daily chess.
Does this mean that "daily chess" is different from a rapid?

the rating you get after every game is dependant on the mode. so if you win in rapid then you gain elo in rapid, if you win in daily chess then you gain elo in daily chess.
Does this mean that "daily chess" is different from a rapid?
the time format is different and the fair-play rules are a little different. if you chose to play daily chess with a time format as one day, you get one day to make a move and after you do the clock resets to 1 day. you can see the rule change here

What is the difference between the "daily rating" and the rating you earn after each game?
Daily Chess is what the site call correspondence chess, where you have one or more days to make each move.
https://support.chess.com/article/361-what-is-daily-chess
What is the difference between the "daily rating" and the rating you earn after each game?