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My own surmise is that the term "energy transfer" is slightly more general: "energy transport" refers to spatial transport of energy (e.g. via conduction or convection), while "energy transfer" also include a transfer of energy in the same position, e.g. between electrons and phonons in a metal.
With regard to differentiating energy transfer by heat vs work, the key term in this definition is displacement. In the case of heat transfer, in no case is there a net force causing a net displacement of the atoms and molecules of the substances involved with heat transfer.
So the linear energy transfer is the amount of energy (per length) the medium receives from the particle, while the stopping power is the amount of energy (per length) the particle loses. The difference between these two is the amount of energy (per length) that is lost to the rest of the environment. These are called radiative losses.
It does not deal with changes in internal energy, and does not consider energy transfer from heat. Work as defined in thermodynamics is a much broader concept and is "energy that crosses a system boundary without mass transfer due to any intensive property difference other than temperature between the system and its surroundings".
When we say that electromagnetic waves transfer energy, we mean that the electromagnetic field has energy stored in it - just like the particles of waves on whater have kinetic and potential energy. Classical view
Given this, a Joule (the unit of Energy and Work) is equal to a Newton (unit of force) * a meter (unit of distance). If a box has had 10 Joules of work applied to it and has moved 5 meters, this tells you that 2 Newtons of force must have been applied. This is all work/energy transfer is: force applied over a certain distance.
For a basic understanding of energy, I like the simple definition of energy stated in an old engineering thermodynamics textbook. "Energy is the capacity, either latent or apparent, to exert a force through a distance." Obert and Young, Elements of Thermodynamics and Heat Transfer.
Work is energy transfer in a form that can exert macroscopic forces on external systems. For example, a hot gas can expand and drive a piston. Heat is energy transfer by means other than work or transfer of matter. For example, thermal conduction can transfer energy from a hot system to a cold one.
Transfer of energy is a concept that makes sense when there's a clear causal relationship between what happens to one object and what happens to another. The sum total of the energy must remains the same, so if one object loses X energy and another gains X energy, we say that energy was "transferred."
Work as well as heat are means of energy transfer. While you may have (or carry og contain) energy, e.g. thermal energy or kinetic energy etc., you can't "have" work nor heat. Heat is what we call thermodynamic energy transfer (miniscule vibrations passed on from particle to particle).