In thermodynamics, heat is defined as the process of transfer of energy.
So you can't ask, how much heat an object has, only how much energy is going in or out of the system during some time period.
The definition of entropy is dependent on the area of physics you are dealing with, in thermodynamics it is defined as $S = k ln \Omega$.
If this looks too maths based for you, read this page Entropy and you might appreciate how straightforward it is, compared to the complications involved in explaining entropy in words.
Entropy is a measure of the number of states a system, such as those in which container of gas might be found in, over a period of time.
The main difference between energy and entropy is that energy is conserved, but entropy is not conserved and will increase over time.