Is the collie the same as the border collie?

No. The breed referred to as just the "Collie" is a very different breed than the Border Collie. In fact, the Collie is usually called a Rough Collie or Smooth Collie, based on whether it has long or short hair.
Some Hollywood examples of each: Lassie was a Collie. Fly from the movie Babe was a Border Collie.
There are other breeds with Collie in the name, such as Bearded Collies, Farm Collies, Scotch Collies. Collie is a general herding type dog description.