The Arizona Cardinals origin of "Cardinals" dates all the way back to the team's origins as the Chicago Cardinals although the name didn't come from the bird but from the jerseys they got that were supposed to be maroon-colored for the University of Chicago's colors, (at the time) however they got cardinal red instead, which led to the nickname in which they moved to Arizona and became the Arizona cardinals.
Here is the history of the teams logo
Here is the history of the teams logo