Gin is a bit of an odd duck when it comes to spirits, since most of the flavors come from additives that are incorporated into the spirit after it has already been distilled at least once. You can read more about it here, but the big differences in the spirits are typically in the level of juniper in the flavor profile and the kind of infusion process that is used.
For an American gin, typically the primary differentiator is that juniper isn’t the focus of the flavor profile and is relatively subdued. These gins tend to focus on other elements while still incorporating that juniper note, allowing for more experimentation and interesting combinations.