in the first principle Thermodynamic, the energy is saved and conveted from type of energy to an other type. So, heat is a form of energy which converted to mechanical o electrical, or kinetic or potential energy.
I would say that (till a large extent) both of the statements are correct; but none of them defines "heat". If what you are looking for is a handy definition, I would offer you the following,
Heat is the energy transferred as a result of a difference in temperature (or a change in phase). And, of course, if what you want is a more precise definition.and insight; I would advice having a second reading of the corresponding chapter in a book of (elementary) Thermodynamics).
The latter attemp of the definition makes appearence as a correct one: energy is the state function, i.e. you are in a position to attribute a certain value of energy (albeit with precision of an arbitrary constant) to any state point, whilst heat is a characteristics of a process evolving between 2 points of the state space. One of the salient consequences of this consists in that dU is a complete differential regarding independent variables of the state space, whereas dQ depends on the trajectory of the process in the state space and can not be resolved as a sum of products of partial tangent times a differential of an independent state parameter. Although U (internal energy) is only a part of the total energy, for fixed external state parameters its surface gives inclusive info about the total energy value....Summing up, heat is a channel of altering energy....
Another short definition could be "heat is a way to change the energy of a system". As Carlos Otero commented previously, it requires a temperature difference or change of phase.
If there is a change of pressure at isothermal process, is there any heat exchanged? Also, if the volume changes at constant Temperature in some proceses, is teher any heat exchanged?
The answer for these questions will help to get a complete definition of the heat.
By definition,, ENERGY is CAPACITY to do WORK. And, WORK is defined as CHANGE of STATUS of Energy of a SYSTEM. Further, by the Law of Conservation of Energy, energy can neither be created ,nor destroyed. Only its form ( status) can be changed; that is, energy can be transferred from one to another system or form within the same system. This process of change of status of energy in a system is work. Heat is a form of energy ( thermal energy ), stored in a system, which can be transferred from one to another system , under a given condition ( temperature gradient ). Heat , as thermal energy , cannot transfer itself from one to another system, unless and until conditions are created for it by doing work upon the system or extracting work from the system( Law of Inertia). So , to sum up,. as your (1) statement says " Heat is Energy" is right. Statement (2) is incorrect, because heat ( energy ) in a system , per se, can not cause transfer of itself
2 ) yes, with heat transfer you ALWAYS transfer Thermal energy (or, more correctly, internal energy) from a body (higher temperature) to another body (lower temperature). There is not heat without energy transfer. There is thermal or internal energy without heat.
.In few words, heat is the "symptom" of thermal energy transfer but is not the cause.
Heat is energy and temperature is a measure of its potential. It flows as ALL form of energy from a higher potential to a lower and we have to say thanks for it since in the opposite situation the world would be unstable.
If you have a body at height H1 it has a potential energy with respect to the height H2
I am surprised that among people of such a high level the question can be given the second definition. It shows a total misunderstanding of the energy and energy transfer as well as potential and potential differences notions.
That a "TEMPERATURE" can be changed by a heat transfer it is normal but "HEAT" is the energy which due to its transfer because of a potential difference moves from a SOURCE to a RECEIVER and modifies both temperatures, i.e. the source will LOWER its TEMPERATURE and the receiver will INCREASE his. This process will stop when both TEMPERATURES are equal since there no more potential difference to allow the transfer.