Loan Assumption

Any 'sale' creates a taxable event when tangible property is exchanged for cash or consideration. 
"Consideration" means recompense or payment which includes anything of value to the parties to a sale. Consideration is not limited to cash. Assumption of debt is a for of consideration.  So therefore, we you assume someone else's  loan or  get a loan for yourself to pay for the vehicle, it creates a taxable event. 

If an additional party is added to the land an the original debtor is not relived of their debt, no consideration has been given and no sales tax is due. 

Encumbered vehicles cannot be given to another party. 
If there is a lien on the vehicle, the lien holder has a security interest in the vehicle and an interest ownership. Therefore, the titled owner can not "give" the vehicle to another party. The vehicle isn't theirs to give away.  The lien must be satisfied before the vehicle can be transferred. If the purchaser gives the seller money to pay off the loan so that their vehicle can be "given" to the purchaser - the vehicle then was not a gift. The purchaser bought the vehicle for the loan amount they gave to the seller.