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.