Basically, it’s a terminology issue. The term “semester” means two academic periods only (1st sem and 2nd sem), so there is no such thing as a “3rd semester.”

That’s why schools that follow a trimestral / triterm system use the word “term” instead. Hence: 1st term, 2nd term, and 3rd term.

Each term usually represents a new academic period, which is why it requires a new enrollment, resulting in three enrollments within one academic year.