Not only are US 120V plugs different than 240V plugs, but the 120V/20A plugs are a superset of standard 120V/15A plugs--a 15A plug will fit a 20A receptacle but not the other way around. I do not believe code permits plugs for devices beyond this range--the really heavy stuff is always hardwired. I believe this is to prevent morons from trying to power their house from a generator with a suicide plug--forcing people to use a proper transfer switch that can't backfeed. I suspect this will change in the future due to how dirty small ICE engines are--as it stands things like electric mowers aren't very good because they can't get enough power to be good. Likewise, pressure washers--the high power versions are always ICE. Where I grew up you needed at least 4hp in a lawn mower--and you can't draw 4hp from a normal wall plug.
You could probably fit an adapter, but I imagine smart plugs in the US are built with the assumption they will never have to handle such a high load.
Maybe not in US. In AU, for example, they do. Also I'm surprised to hear that. I would have expected them to be universal and work anywhere between 110 and 240V.