Hey, I remember being confused by chicken breasts too!
Technically a chicken breast is both halves. So a bone-in chicken breast piece is often called a "split breast". BUT whenever I see a boneless chicken breast in a recipe, it's always referring to the split/half portion. I can't recall ever seeing a recipe that wants you to use both halves to equal a "chicken breast".
However, to make things more complicated -- a typical serving of chicken breast is 3 - 4 ounces and sometimes a half breast is double that (6 - 8 oz), so then half of a half breast is a normal serving size.
Have I confused you further?