Does this make sense from mass-energy equivalence standpoint? Over the weekend I was (in over my head) discussing mass/energy and I proposed this thought experiment.
Given two separate but equal quantities of matter - one being wood, the other being gasoline - do they both have the same total energy? I am being assured that the gasoline has more every than the wood but if the mass is equal shouldn't they have the same theoretical energy? What is the name for that type of energy? Is it simply a matter of the gasoline being in a form that is more readily extractable (explosion vs burning)?
 A: It depends on what you choose to consider as energy.
Using mass-energy equivalence as your logic seems to be, then theoretically two objects of the exact same mass will have the exact same energy.
If we want to consider how we will extract this energy, most would say that gasoline has more available energy than wood.  That is to say, we don't usually convert wood or fuel into pure energy (this would be impossible with our current technology AFAIK).  
When we talk about the energy in fuel sources like this, we generally mean the usable energy; which we put into practical limits of how we can extract the energy.
The common example for wood and gasoline is by burning them.  This is a chemical reaction that takes energy that was bonding the molecules and instead the bonds are reformed in a lower energy state, releasing the difference (mostly as heat).  It requires a bit of heat to start this reaction; but then the heat generated from the reaction is enough to keep the reaction going as long as their is enough oxygen.
Releasing this chemical energy will lower the masses slightly; but the mass-energy equivalence makes it so that this mass change is quite small compared to the mass of the combustibles (because in the end of these reactions you still have molecules which still have mass, so you will not be extracting all the energy from the mass-energy equivalence principle).
A: What is storing energy?
There is a mass-energy equivalence, which since they have the same mass is equal. We have no idea how to get anything but trivial fractions of this energy through the below mechanisms.
There are nuclear bonds, which since they are both mostly hydrocarbons are probably pretty similar, though having different fractions of the different elements will mean there is a difference. We can make nuclear reactions, but wood and gas are not used in any known fusion or fission process.
There are Chemical bonds, and here we get interesting differences. We can break those bonds and then the energy released from the bonds is more than it costs to break the bonds, and a chain reaction happens. Gasoline has more energy in it's bonds than wood (why it burns better).
The chemical bonds are trivial to the nuclear bonds and the nuclear bonds are pretty trivial to the energy-mass equivalence, so if you made a not quite strict accounting the energy could be said to be equal because all the chemical and even nuclear energy could be rounded off. But if you mean usable energy only the chemical energy is at all important so the gasoline has more.
