So I understand that civilian car manufacturing stopped once WW2 started but what were some of the advances that happened between the time that WW2 started (and civilian production halted) and when civilian car production started again after the war thanks to advances made during the war in technology?
Tl;dr : Competition, production efficiency and the fact that planes don't need infrastructure (like cars need roads) to reach high speed.
On airplanes
First things first, jets are older than WW2, if only by a few days. The first functional jet aircraft, Heinkel's He 178 flew in 27th August 1939, a few days before Germany's invasion of Poland.
There's two important jumps here to address, one from biplanes to monoplanes, and the second from propeller to jet engines. Both of them were conditioned by the operational doctrine.
The doctrine here is the emphasis on speed. In the interbellum period, certain air doctrine theorists argued that fighter aircraft are already obsolete, and that the future of air power lies in quick, uncatchable bombers.
Larger powerplants allowed us to switch from biplanes to monoplanes, allowing a more powerful engine to provide enough lift on a single pair of wings and lower drag. The switch from propeller to jet engine was bottlenecked by matters of fuel efficiency. The size of the fuel tanks and the efficiency of early turbojet engines didn't allow for a sensible design and combat performance with an operational range counted in minutes.
Given the competitive context of air superiority doctrine, if your enemy has a faster, more powerful plane than you do, you are in quite a pickle. So technological advancements during the war were focused to squeeze the most efficiency out of its engineering and manufacturing in order to get an upper hand over the enemy.
On ground wheeled motor vehicles
Meanwhile, the wheeled vehicles used during the war were mostly trucks, used to supplement or replace the traditional horse-drawn carriage and not used in direct combat situation (with the exception of a few armored cars like SdKfz222, M8 Greyhound, Ba-10 and AB41) As such, they had to be produced en masse, in order to motorize the existing horse-drawn carriage supply lines. If you had a working truck that could get supplies to its destination, investing time and resources into R&D to make it faster or better performing is a waste. This also means that a new 'type' of truck is going to need its current production stopped, in order to amend for the changes, and that simply can't happen. Also, the bottleneck of supply lines was usually the state of the roads a truck can use. Having a 120km/h truck in the middle of a muddy eastern front field is as useful as having one that can go 20km/h - they'll both move at a same speed.
If you're looking at the development of civilian motor vehicles, you need to look at a competitive situation as well, like the interbellum car racing designs which gave us engineering works of art like Mercedes-Benz W125, which, manufactured in 1937, could reach speeds of 300km/h.