There are different types of turbines,
-Single Stage
-Tripple Stage
-Free power contra-rotating turbine,
but they all operate in the same principle.
These are but a few of the many types I've encountered.
First - identify how many independent spools there are in the engine:
e.g. Single spool - J85, J79, TPE331, T56 etc.
Twin spool - J57/JT3D/JT8D/JT9D, CF6, T58, T64, CT7, PT6, PW120 etc.
Three spool - RB211, Trent etc.
Each spool rotates mechanically separate from other spools in the engine, therefore each spool needs a turbine section to drive it. A twin spool engine has 2 sections - High Pressure and Low Pressure. A three-spool engine adds an Intermediate pressure section.
Each turbine may have from 1 to 6 or 7 stages of blades.
And they may all rotate the same direction, or counter-rotate.
So just the basic type definition must consider all these factors.