Grossly wrong.
A law says that you have to pay Smith, or Brown.
Everything you just posted is that the Government demands the money, then it spends it.
Totally different. Different parties, different methods.
After a while, Congress, so that it doesn’t have to be involved, will authorize private companies to tax you.
In short, you will be sold, partly, to private companies.
Supposedly for a service.
Since you have been thus sold, by force, you are, or part of your income, choice, liberties are owned by that company.
You may not have noticed but they have been doing that for years, by allowing hospitals and doctors to overcharge people with insurance in order to cover the expense of people with no insurance. It is a well known fact that most in these forums conveniently overlook. Not saying it is right, just that it is a fact I have known about since the early fifties.