What distinguishes chest pains due to indigestion and a heart attack?

Nobody really knows: Risk factors such as hypertension, family history, high ldl, high BP and diabetes are important.

Hard to tell: These pains may be very hard to distinguish: indigestion usually occurs after meals, especially if spicy or fatty; heart attack pains usually occur with exertion, may be associated with shortness of breath or radiate down the arm. It is really hard to tell, unless you are in a hospital setting where the necessary tests may be done. Especially in women.