U.S. states were / are a lot like EU countries. Lots of autonomy. The federal government doesn't control everything like it would in say, France. It only has a certain sphere that it's supposed to operate in, and the rest is the domain of each individual state. This is good because it allows different areas to self-govern themselves as they wish within reason, while major issues (eg. bill of rights) are non-negotiable.

For awhile now however, the federal government has been grabbing power using things like the interstate commerce clause to control what would traditionally be a state's sole responsibility to handle.

Anyway, basically states can choose electors however the fuck they want. These electors then get together and cast a ballot for each of their respective states. Mostly this is done via popular vote, although some states split their electoral votes, and others recently have proposed things like casting their electors for whoever wins the popular vote nationwide. As far as the country is concerned, a state can vote however it wants to and its up to each state to determine how that will be.

That's what kind of leads to the clusterfuck of 50 different systems for determining votes. However, it also prevents stuff like the federal government ramming insecure electronic voting machines on the entire country and using those to steal every election.