Maybe Loach or one of the other cops can help me out here, but I always assume that those are usually felony stops- cop ran your plate for something minor and Oh Looky Here- warrant, failure to appear, whatever. So now the driver cools his heels on the curb in cuffs (just for my own protection, son, not because you’re arrested or anything…) while multiple cops dissect his Camaro.
The term “felony stop” refers to something specific. It is basically the way you tactically stop a car that may contain a dangerous suspect. It includes guns drawn, instructing the suspect through the PA, etc. It is a very small percentage of all stops.
There are a few different ways that a car may be searched without a warrant. There is a search subsequent to an arrest. Suspect gets arrested and the area immediately around them gets searched. There is a search with probable cause. The suspect was seen hiding something under the seat. A large cloud of non-tobacco smoke comes out of the window… There is a vehicle inventory. When a vehicle is impounded the contents may be inventoried. If a department does this they better do it for every vehicle they ever impound. They can’t be selective with only dirtbag’s cars. Then of course there is the consent search that has been discussed here.
All of these have been changed or modified through the years by various court cases. What is allowed is also different from state to state. I work in New Jersey and the State Supreme Court tends to make things much more restrictive than SCOTUS requires.