Luggage generally refers to multiple items, including suitcases, hand baggage, backpacks, etc. used to carry clothing and other items when traveling. "How much luggage do you have?" "Do you have all your luggage?" A suitcase is a single piece of luggage, generally larger than a carry-on bag. "Is that red suitcase yours?"

A suitcase is the hard square box type of bag. Luggage can be any type of bag. And baggage is unwanted luggage.

Just something to add - 'luggage' is the same as 'baggage'. Both of these words are grammatically uncountable, while 'suitcase' is countable. Some luggage. A suitcase. How much luggage? How many suitcases?