There are two types of daisy flowers, the Common or Lawn Daisy (the one you'll find populating lawns throughout much of Europe and the Americas), and the other members of the aster family that include chrysanthemums, dahlias, zinnias, gerbera daisies and calendula. So many types of daisies, so many flower meanings.
Different type of flowers symbolize different wishes; this article about the meaning of flowers for the month of October describes what message you'll be sending when you give October's birth month flowers to someone who has a birthday or other event in October (the calendula is the birth month flower for October; the alternative is cosmos flowers.)

