Is there a difference between an exothermic reaction and an exergonic reaction

I only real difference to me would be that exothermic is specifically referring to heat while exergonic could be any energy flow from the system to the environment (ie.- maybe all exothermic reactions are exergonic but not all exergonic reactions are exothermic (could be other forms of energy beside heat)).

Your teacher is wrong, but at the same time I can see why he/she would dodge the question:

I think the term you are looking for is either "exothermic" or "exergonic".

An exothermic reaction is one whereby energy is released from the system into the environment usually in the form of heat or light. The converse is an endothermic reaction. Both of these reactions relate to the enthalpy change of the process.
An exergonic reaction is one whereby energy is also released from the system into the environment. The converse is an endergonic reaction. Both these reactions relate to the Gibbs free energy change in the reaction.

I would like to point out that if "an action produces more energy than is used to prepare", the additional energy that is produced would have to come from somewhere else--usually it is from the chemical bonds within the molecules. In other words the energy was already there in some form or other.

• “Exothermic” and “exergonic” reactions are both chemical reactions in the field of thermodynamics. These terms are commonly used in the physical sciences.
• “Exothermic” literally means “outside heating” while “exergonic” literally means “outside work.”
• Some examples of exothermic reactions are: combustion of fuels such as wood, coal, oil, and petroleum, condensation of rain from water vapor, and mixing of alkalis and acids.
• Some examples of exergonic reactions are: catabolism, respiration, and the breakdown of sugars through cellular metabolism.