Luggage and baggage (check the spelling) are uncountable collective nouns. Suitcase is a singular noun, so refers to one item of baggage, and is a specific type and size of bag. Luggage and baggage could be one or many suitcases, and could include your carry-on bag, and possibly other items, such as boxes, and sporting goods bags. I think that luggage and baggage might be more common in Britain and the USA respectively. Or maybe it's the other way around? ;) We use both interchangeably.