Baggage is a general term for things carried with you:
Bags, luggage, back packs, kids, purses, old relationships that still crop up, exes (wives husbands boyfriends girlfriends that still call) things you have done wrong that will crop up in your life, handbags.
Luggage is a type of case like a suitcase, which often holds its shape without items in it - not so often a bag.