There is no significant difference in meaning between luggage and baggage. The difference between suitcase and luggage/baggage is mainly a grammatical one. A suitcase is an individual item of luggage, in just the same way that a ring is an item of jewellery. A suitcase is a single object, while luggage and baggage are collective and general terms to refer to everything you carry with you when you are travelling. If you are travelling, your luggage/baggage can be bags, suitcases, backpacks, sports equipment - or anything else that you are travelling with. The word 'suitcase' is grammatically countable. It can be singular (a suitcase) or plural ( two suitcases). How many suitcases do you have? The words 'baggage' and 'luggage' are grammatically uncountable. They are always in the singular, but they don't take a singular article (a). We can say 'some luggage' , but we can't say *a luggage and we can't say *luggages. How much luggage do you have? I hope that helps.

They all mean the same. A suitcase is luggage or baggage.

I would say that suitcase is more of a single item. "I have a suitcase" "I'm packing my suitcase full of beach clothes" Baggage or luggage is more of a plural term for "suitcases" at the airport or while transiting. I would never say " I have to pack my baggage" or "Have you packed your luggage?" But I would say "We have to pick up the baggage" say if you were traveling as a pair and you both checked your "suitcases" or luggage. suitcase: more formal, singular, at home, (usually rigid and boxy) luggage/baggage: more plural, at an airport or train station, usually leathery with a shoulder strap or a large black roller