Here in Montana, if you buy from a dealer, the dealer prints a 40 day permit, the paperwork is delivered to the DMV Office (I think the dealer makes that trip once a week) in the County Courthouse, and the Office sends you a postcard saying they are ready to transfer the title and register your new vehicle. You go in, pay the fees, get (or transfer) the plates, and they tell you you will get the title in 4 to 6 weeks. Lately, I have found it takes about 2 to 3 weeks.
If it is a private party sale, YOU take the signed title to the DMV office, pay the fees, and transfer or get new plates. The Bill Of Sale and/or signed title is your 40 day temporary permit.
Just do not use a credit card to pay the fees. There is a surcharge for that!