Yes, there is a major functional difference between internal and external combustion engines

Internal combustion engines cause energy through the oxidation of fuel while external ones cause energy to be delivered to a working fluid

Combustion occurs externally in the case of External combustion Engines. Probably it may be in a external combustion chamber. The gases from that are used for driving the Engine.

In the case of Internal combustion Engines the combustion occures internally and also used internally to drive Engine.

External Combustion Engines are better because combustion and gases can be taken care of individually like cooling, continuous operation. In the case of 4 or 2 stroke Engines Intermittent firing takes place. This can be overcome in External combustion engines. And better control over fuel flow and ignition giving overall better performance not depending on the no of strokes.
Example: Separate Compressor, separate Combustion chamber and separate Cylinder or Rotor with nozzle.
The IC Engine which comes close to this is Turbo Engine (Turbo charger with burning in between compressor and Turbine. Typical aircraft engine).
The benefits in case of External combustion Engine are better placement, cooling operational control.