I'm referring to what's listed on Amazon under the configuration. Here's an example: https://www.amazon.com/Tamron-28-75mm-Aspherical-Digital-A09NII/dp/B001955P8W/ref=sr_1_4?s=photo&ie=UTF8&qid=1473506919&sr=1-4&keywords=tamaron
"US Version" lenses are imported into the US by the official distributor. They come with a US warranty.
"International Version" (also called "gray market") lenses have been (legally) imported into the US by a third-party. But since these lenses were not intended to be imported into the US by the manufacturer, they come with a different warranty, which may or may not be valid in the US. In case the warranty is not valid, sometimes the third-party importer will offer a third-party warranty instead.
In either case, the lens itself is the same.
Addendum: I just noticed that Amazon explains this themselves right on the page:
This [International] version is originally intended for sale outside the US and may contain adapters, manuals, and warranties not compatible with US standards.