Acid indigestion is a type of indigestion involving an excess of hydrochloric acid in the stomach. Acid indigestion should be distinguished from heartburn, which typically involves aggravation of the esophagus.
When you're checking wikipedia at 3AM for differences between these two conditions while doubled over in stomach pain after having a pepperoni and jalapeño pizza and a couple bottles of of Dos Equis Amber at 9PM, and drinking another one to help "neutralize" what you have, since it's the only carbonated beverage in the house, you need to know where your esophagus is.
It's just below the breastbone, so if your pain is lower, it's probably acid indigestion. When this happens, your best bet is to try to neutralize with carbonation, wait for Montezuma to exact his "revenge" on your gastrointestinal system, and swear off spicy foods "forever". By which I mean the next 24 hours. What's the point in living if you can't eat pizza and drink beer a couple of hours before bedtime?