mt car title is showing as the lein has been satisfied. i still owe money on it. do i own the car?

You already owned the car, just subject to a lien, like owning a house subject to a mortgage.  The lien may have been wiped out, and you may now own the car free of any encumbrances, depending on why title is showing the lien as satisfied and whose fault it is that the mistake was made.  However, that doesn't mean that you don't still owe money.  The lien just secures the underlying debt, it is not the debt itself.  Wiping out the lien doesn't wipe out the underlying debt, it just means it will be a little more difficult for the creditor to collect on it if you default.