Do people in the US understand that republicans and democrats are all part of the same organisation behind the scenes?

I see a lot of debates going back and forward between republicans and Democrats but I don't understand why they seem blind to the fact that both parties are owned by the same organisation. It's a system that is set up to make you feel like you have a choice but you really vote for exact the same organisation no mather if you choose to be republican or democrat
Do people in the US understand that republicans and democrats are all part of the same organisation behind the scenes?
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