Comment by JumpCrisscross

> I am unsure all visible fans on modern jets on the spool couple directly to the turbine

They exist now [1][2]. The general term is geared turbofans.

If you want to mentally unfuck it a bit, the major variables are: combustion type (internal or turbine), gearing or not, ducting or not and bypass ratio. (Compression ratio and number of blades can come too.)

When one of these changes substantially, you get a change in engine type. When it changes a little bit, you get a blur.

[1] https://en.wikipedia.org/wiki/Pratt_%26_Whitney_PW1000G

[2] https://en.wikipedia.org/wiki/Rolls-Royce_Trent#UltraFan