Right, but the "probable cause" is technically different -- for a search without arrest, they need probable cause to believe that there is contraband in the car, for arrest they need probable cause to believe you have committed a crime. Given that possession of contraband is itself a crime (though generally one with a mental state requirement), there is quite a lot of overlap between the two kinds of "probable cause", but they aren't equivalent.
I won't repeat dragonwriter, but I wasn't criticizing, just pointing out that your statements aren't absolute rules. They just tend to be the simplest statements of the rules that exist.
Also with arrest, lower standard for if they think evidence will be found. It's the RAS-like "reasonable to believe" that evidence of the crime will be discovered.
