The breed originated in Ireland, but it's been popularized worldwide and there's no separate lineage or breed standard for a specific "American" version.
Some people might use the term "Irish" in their name or description, but it's simply a way of emphasizing the breed's origin, not a separate breed classification.
Here's what to remember:
* There's only one breed: Soft-coated Wheaten Terrier.
* The breed standard is the same worldwide.
* "Irish" is simply a reference to the origin, not a separate breed.