Well... yes, they are groups of people, but governments are rather different. Governments include everyone and act on their behalf. They are also responsible for creating and enforcing law. The distinction is valid.
It's more accurate to think of governments as a special case of corporations.
Governments don't always "include everyone", and as we've seen, they definitely don't necessarily act on their constituents' behalf.
In certain contexts, corporations have also been responsible for creating and enforcing law, even though that's not the context we are used to today in the US.