This is a questions i see quite a lot in various forum posts. It is a trickey one to answer too.
Pekin is a true bantam breed, that does not have a large fowl equivalent. They are the same as a Cochin bantam. Large fowl Cochins are NOT a large version of the bantam though. They are breed designed around the same charateristics, but bred from different varieties to achieve that.
If you shrunk or "bantamised" a large fowl cochin you would not get a Cochin bantam as we know the breed today, they are an entirely seperate breed.
The difference in the naming conventions is rather strange, here in South Africa and across europe the birds are called Pekin bantams or Pekins, in the USA they are known as Cochin bantams. Those are two different names for the same little fluff balls we know and love.
Hope that has helped to clear things up a little,