These words are the same. Both of them refer to the collection of suitcases/bags you take with you while traveling.
Both of them are uncountable nouns, so don't use "a" or make them plural:
I have three luggages.
I have three pieces of luggage.
I accidentally left a baggage at the hotel.
I accidentally left a suitcase/bag at the hotel.
I accidentally left a piece of luggage/baggage at the hotel.
The place in the airport where you pick up your bags after arriving at your destination is called the baggage claim. But when the airline loses your bag, we usually say they lost your luggage (not baggage).
The word baggage has an additional meaning: emotional or psychological effects from the past that negatively affect your present situation. For example, if you had a past romantic relationship with someone who lied frequently and now you have problems trusting anybody, you have "baggage" from that relationship.
This is a beautiful shades of red and white Chunky Necklace and Bracelet set. This chunky necklace has a variety of chunky beads and has a lobster clasp. A 2 extender chain can be added if desired. If you would like this feature please make note of this in checkout. Bracelet is stretchy and is made to fit under 7 years of age. If you need this for an older child please let me know and I will include a larger bracelet for ages 8 and up. This set is perfect for your little princess. All of my chunky necklaces measure approximately 18 and will fit children and some adults. This is ready to ship.