Logical models show what a system is or what a system does. They depict independent of technological implementation and in that sense illustrate the essence of the system.
Physical models on the other hand not only show what a system is or what it does, but also show the system is physically and technologically implemented.
Thus the difference between the two is in their implementation. Logical models are implementation independent and physical models are implementation dependent.
For example, logical models are necessary when you when you want to connect a problem to the specifications needed to solve that problem. Physical models are needed when converting those specifications to actual hardware. A logical model describing a customer would have different attributes about that customer that a business can assess. The physical model for a customer would contain implementation details so a business can use that information and put it into action.