If you google one you will see they are the same
Calla is the common name, the z. word the botanical name
Karen

Karen is right, they are the same. Also called Arum Lily, or Pig lily. In the US most people call them Calla Lilies, in Europe most are called Zantedeschia or Arum (arum in not a correct name, though).
There is a little argument over how to pronounce, I say
Zan- teh- desh- ee- ah or Zant eh desh ee ah.

The large white ones and Green Goddess are grown differently from the colored ones, though. They are bog plants, and rhizomes, whereas the colored ones are bulbs (or tubers) and like to be drier in between waterings.

It's fine to cut off the flowers, gives you strong bulbs. You can also leave them on to make seed.

Hope that helps!
Susan