The taxi driver says 알겠습니다 but the lesson teaches 알았어요. Why the difference?

Both are polite. Staff serving a customer usually use the more formal -습니다 style: a driver, a cashier or a receptionist speaking to a customer sounds right that way. It is a difference of situation, not of politeness level. You can keep answering in 해요 — you are the customer. At this stage recognising -습니다 matters more than producing it.