I don't think there are any American-made batteries or cells. Do we actually still make anything that you can buy without being asked, "Do you want fries with that?"
Most are made in China. I'm not even sure whether any are still being made in Japan; most of the Japanese brands (e.g., Sanyo) have switched to Chinese manufacturing.
With coin cells, there is a *huge* difference in capacity between the well-known brands (e.g., Duracell, Energizer, Panasonic, Rayovac, Sanyo, Varta) and the "off" brands or no-names. I expect that this is also true of button cells, but I don't have evidence of that.
I think the well-known brands I listed above actually do their own manufacturing. I'm less sure about Maxell, Renata, Seiko, and Sony; it seems possible that they may be OEMing cells from another manufacturer. That's not necessarily bad, depending on the manufacturer, and they would presumably be motivated to choose a manufacturer with a high-quality product.
On the other hand, the less well-known brands and the no-name stuff are made by companies we've never heard of, and their concern over product quality and performance is substantially lower.