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.

Forever Young Naturally Exercise

Hand and Foot Mobility Foot reviver

Start by kneeling, then tuck the toes of your right foot under. Step forward with your left foot and gradually take your bottom toward your right heel, increasing the stretch on the back toes. Repeat on the other side. Try this for stiff, tired feet, but if you find this exercise uncomfortable, exert pressure very gently.