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.
One of the major causes of dark circle is heredity. You are most likely to develop dark circles if your parents also suffer from the same. It happens because your family might have a tendency of having thin skin layer around the eyes or having more blood vessels than the average lot. Or, both the cases can be present. This leads to awfully bad dark circles.