As Bill stated, same transmission with minor differences.
The car trans mounts with 4 bolts into the bellhousing. The lower bolts on the truck thread into the trans. Just use a longer bolt with a nut. The side cover is different, use the side cover from the truck. While you have it apart check the 2-3 shift fork. It is a common wear area and can cause popping out of gear. There may be a difference in the spedo gear also. Some of the early trucks had a metal spedo gear, it will not work in a car trans. You should be able to find a suitable plastic gear to match your rear end ratio.
Fred


1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine