Where fan /compressor air passed along the outside of the powerplant casing then this engine was called a turbo -fan
Virtually all of the large high-by-pass turbofans fitted to commercial transport aeroplanes fit this definition.
But if you look at the majority of the engines fitted to modern fighter aeroplanes, the situation is completely different.
When you open the MVP bag to take out the replacement engine, you find a large cylindrical object that comes complete with the fan, engine core, by-pass duct and reheat system. In the UK this cylindrical object is commonly called an "Engine Change Unit" (ECU). But these engines are still called turbofan engines.
If we want a description that fits all types of turbofan we need to use something like.
1. The hot air stream passes through the engine core. Some of this air is used for combustion and some is used for cooling.
2. The by-pass air stream passes around the outside of the engine core. This air by-passes most of the compressor stages and all of the turbines.
3. In some turbofans the hot and cold streams are mixed back together inside the jet pipe and in other turbofan the mixing takes place externally.