Casually/vernacularly, though not academically, many Americans just use "Victorian" and "Edwardian" if they're referring to the mid-to-late 19th or early 20th centuries.

When people do need to make sure they're referring to the specific American context, there are no equivalents. The Victorian era covers the reign of Victoria, 1837-1901, which has real political meaning in the UK but not in the US, and the same with the Edwardian era/Edward VII's rule: why would 1837-1901 be an epoch in American history?

If referring to a time period within that range, there are a number of terms to use depending on the context. The antebellum era, for instance, can run from the beginning of the republic to 1861, the start of the Civil War. Andrew Jackson's presidency (1829-1837) is sometimes referred to as the "Age of Jackson". Reconstruction is 1865-1877, and the Gilded Age follows it to the turn of the century. These are all political terms - in art and fashion, we frequently use the names of prevailing decorative arts movements we're referring to rather than a political era.

There were a ton of cultural similarities, in large part because the world was smaller than it used to be - more texts on manners and fashion periodicals were being published, and they could be transmitted back and forth more quickly. Upper-middle- and upper-class American society was also descended from England and felt that quite keenly. While American-printed etiquette books might talk about how American manners were freer and more equal, the actual conduct they describe tends to be pretty much the same, particularly in the second half of the century.