Lien is a record that can be put on your asset, meaning that any sale proceeds of the asset will go to a lien holder/lien holder must approve any transfer of ownership. The asset continues to belong to you though.
Loan is when someone gives you money and you promise to pay it back.
Mortgage is a specific case of a loan - loan is called "mortgage" when something is mortgaged in return (usually this refers to real estate, but auto loans are essentially the same). I.e.: the lender puts a lien on the property and has the right to sell it if you're in default on your loan obligation (a "regular" lien doesn't give that right).