Gratitude is an emotion from the heart. Gratitude is where you are thankful something happened but aren't required to give back to the person who helped you. It's for the simple things, like, dropping your wallet and having someone return it to you. Some one opens the door for you and you thank them. Gratitude is for the little things people do that you offer thanks for, but would don't leave you with a feeling of needing to do something nice for them in return.
Indebtedness, on the other hand, seems almost as if it is higher than gratitude. Indebtedness is where you are so thankful for what the person did, whether it be saving your son's life or persuading you not to commit suicide, you feel a need to give back to that person in some way. Sometimes it can be a simple case where a really nice person drops their wallet and you return it to them. They then say, "how about I grab you lunch since you were so nice as to give me back my wallet." That is indebtedness. You have a need to return the favor for what another person did.
Now, another difference between gratitude and indebtedness is the fact that gratitude is alway positive. Indebtedness can be both for positive and negative depending on the circumstances. Think in the terms of Hammurabi's code, "an eye for an eye." If someone were to kill your mother, you feel the need to get revenge on the murderer. That is indebtedness. You are indebted to the murderer for what they did to your mother, so how do you pay off that debt? You kill them back, or do something so awful to them they wish they were dead. That is just a blunt description in what negative indebtedness is. Another way to describe it is, someone punches you in the face so you punch them back. You two then get into a fight and get tossed out of your favorite bar. Because he hit you, you felt the need to his him back. Because you guys were agitating people and causing a ruckus, the bartender felt the need to toss you two out. Indebtedness is almost like cause and effect. You do something and someone or something pays you back for it in someway. In other words, you can describe it as the consequences of your action.
There are probably many for ways you can take these two concepts, but that would probably go on for a long time. Either way, indebtedness leaves you feeling in need to treat the other person in equivalence of how they treated you, and gratitude simply leaves you happy and thankful for something that happened. One can stem off from the other, creating an easy confusion between the two. Sometimes, when a person has a high moral code, gratitude is the exact same thing as indebtedness. It just depends on from which perspective you are looking at it.