Help?! English terms regarding airports and Air travel?

So, this is the issue.. The "carry-on bag" is a bag that you can keep with you on the plane, right? And then "hand baggage" is the exact same thing? Cause in my country the equivalent of hand baggage (I mean if translated literally) is luggage that is checked and therefore you cannot take with... show more So, this is the issue.. The "carry-on bag" is a bag that you can keep with you on the plane, right? And then "hand baggage" is the exact same thing? Cause in my country the equivalent of hand baggage (I mean if translated literally) is luggage that is checked and therefore you cannot take with you on the plane. Also, hand baggage is used to differentiate between this smaller piece of luggage that does not require you to pay any extra fees, and a larger, heavier suitcase for which you need to pay more money. So.. Am I missing something? If carry on bag and hand baggage are the exact same thing and that s the bag that you take with you on the plane, then how do you differentiate between the two other types of luggage that are checked and cannot be on the plane with you? How do you call them?
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