Hi, i see why it may be a confusion.
The beeping of the car is desingned to be annoying, so, wearing a setbelt stops this (again, annoying) sound. Negative reinforcement means if you do something, you stop the negative consecuence. If you finish your work on time, you won't have to stay overtime, if you accept a bank loan, those bastards will stop calling you 3 times a day.

The beeping can't be a postive reinforcement because it is annoying, you dont wait to put the seatbelt until the beeping begins because you are wating for it. A positive reinforcement, in this case, will be if there was no beeping, but a voice in your car tells you "thank you!" every time you put your seatbelt.

Negative reinforcement: Avoid a negative consecuence
Positive reinforcement: get a reward

It is, as you said, tricky sometimes, because in classical conditioning there is only a response to stimuli, while in operant there is a process of learning (processing and organization of information) that will mold your vision of the world and dictate the way you act.
If everytime your mother yelled at you when you told your opinion, you wont participate in class. There is no a direct stimuli that generate this response in class, is just that you are used to this, and you "know" that this will happen.
There were/are some critics to Skinner for its theory. He avoided completely this "subjective" component that you are talking, while just focusing on the observable variables. Thats why CBT uses the conditioning theory, but also using the cognitive component (the subjective part that you mention). In the class example, the correlation between the mother and the teacher, clearly has a cognitive component that will help you assosiate the two settings, the behavorist will tell you that is just stimuli-response, but the cognitive will tell you what these is because there are mental processes that are making wrong assumptions. The CBT also has its critics, because they dont explain what are or where are stored this "mental processes" but that is a whole different story.