The Legislature and the State also decide who will be on the ballots and whether write-in is valid.
Yes, it is complicated.
The UK and Canadian systems are so much simpler.
In Canada, parties select a leader. He is their spokesman, leads their party in the Legislature. He, like the other legislative members, has been elected by the electorate of his province. In an election, if his party wins, he becomes prime minister; if not, he remains in the Legislature as a leader of 'the loyal opposition. If he is voted out in his province, he may quit, or elect to run in a secure riding from which that member withdraws. This is oversimplified, but may help Americans understand the more straight-forward system in Canada.

The states that came together to form the United States reserved many facets of governance- forming the Union involved compromises.
Systems thus are not uniform.

Dictatorships are in NO way similar; they would tell the states to conform or else!