> In the US both of those would have been handled with an Investigatory detention - same as being pulled over for a traffic stop. Not even remotely an arrest.
I'm not from the UK, but it seems likely that this is just a question of semantics. Many US traffic stops are far more stressful—and handled in a way that is far less conciliatory—than the "arrest" that OP describes. It doesn't sound like they were taken to a police station or even necessarily handcuffed, more just formally detained.
As for US detentions: It doesn't especially matter if they're not technically "arrests" in US parlance, you're still being stopped by the police and you still can't go anywhere until they let you because there's a too-high probability that they'll find an excuse to make your life miserable if you don't cooperate.
I'm not from the UK, but it seems likely that this is just a question of semantics. Many US traffic stops are far more stressful—and handled in a way that is far less conciliatory—than the "arrest" that OP describes. It doesn't sound like they were taken to a police station or even necessarily handcuffed, more just formally detained.
As for US detentions: It doesn't especially matter if they're not technically "arrests" in US parlance, you're still being stopped by the police and you still can't go anywhere until they let you because there's a too-high probability that they'll find an excuse to make your life miserable if you don't cooperate.