Who exactly are you paying your down payment to?

When financing a house or a car and you make a down payment are you giving the down payment to the lender or are you paying the previous owner so that you'll have to borrow less from the lender?

For Example: I want to see a house for sale online i contact the agent for a viewing. If I like it and want to start the process whats the first step? Say the house it $60K, I'm already approved for a loan of up to $100K, I want to put down $12k. Who do I give the $12K check to?
Added (1). Also when you buy a house and its not paid for yet how do you transfer it into your name and once you do pay it off how do you receive a deed? Or do you have a deed from the beginning with a lien holder on it like a car title that's not paid off?

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