Hello.
According to me, and a little bit of searching on the topic, Work in physics generally refers to Mechanical Work, which can be defined as the energy transferred by a force to the system, when the force moves the system through a distance.
A generalization of this Mechanical work is the Work in Thermodynamics.
The Work done in thermodynamics, can be called as the work done on the system, that changes the external mechanical make-up of the system. For example, work is done on the system when heat is provided externally and a gas expands and pushes the walls of the container outwards. Here, in a way, the expansion of the gas changes the mechanical make-up of the system by expanding it. Thus, in Thermodynamic work, heat can be regarded as the force, and the change in the physical structure of the system can be considered to be the distance through which the system moves. And the work done is the energy transferred into the system to accomplish the final state.
Heat, IMO, is the energy transferred to or from the system when another system with a different temperature is brought in some form of association, which can be contact (as in the case of conduction). Now since Work was the energy transferred in changing the mechanical make-up of the system, Heat might be the energy transfer that takes place at the molecular level, i.e. transfer of energy to the molecules due to which their energy increases.
Since increase in energy of the molecules helps in changing the external make-up of the system as well, heat energy transferred to the system is also the basic reason why the entity of work exists, or as i earlier quoted, heat can be regarded as the force.