What is the correct name for this breaker?

[Scott Danforth]

Would it matter in a simple 2 terminal breaker?

Yes. Even the small carling thermal breakers are labeled

 

[nola mike]

Yes. Even the small carling thermal breakers are labeled

Huh. That doesn't matter sense to me based on my knowledge of how they work. Looks like it's time to jump down a rabbit hole.

 

[Scott Danforth]

Notice the two colors of lugs on the small breakers.

The copper lug is the batt connection