Actually, it doesn't matter whether you are a Private pilot or an ATP, the requirements for a type rating are in the Airline Transport Pilot and Aircraft Type Rating Practical Test Standards, which apply regardless of the aircraft type.
In the PTS, it says:
Practical Test Book Description
This practical test book contains the Airline Transport Pilot and
Aircraft Type Rating Practical Test Standards—Airplane. The Airline
Transport Pilot and Aircraft Type Rating Practical Test
Standards—Airplane includes Areas of Operation and Tasks for the
initial issuance of an airline transport pilot certificate and for the
addition of category, class, and aircraft type ratings to an airline
transport pilot certificate. These Areas of Operation and Tasks also
apply for the issuance of an airplane type rating to a private or
commercial pilot certificate.
You basically cover everything needed for the ATP. The differences between the different airplanes come out during the practical test just like they do for any other checkride. The examiner (who will be typed in the airplane) asks you about the things that are specific to each airplane, but this isn't really a lot different than him asking you questions specific to a Cessna or a Piper during your private pilot checkride.
The PTS specifies general Areas of Operation's instead of saying exactly what needs to be tested for every aircraft type.
Here they are for a type rating:
Section 1: Preflight Preparation
Areas of Operation
I. Preflight Preparation
Task A: Equipment Examination
Task B: Performance and Limitations
Task C: Water and Seaplane Characteristics (AMES/ASES)
Task D: Seaplane Bases, Maritime Rules, and Aids to Marine Navigation (AMES/ASES)
Section 2: Preflight Procedures, Inflight Maneuvers, and Postflight Procedures
Areas of Operation
II. Preflight Procedures
Task A: Preflight Inspection
Task B: Powerplant Start
Task C: TAXIING
Task D: Sailing (AMES/ASES)
Task E: Seaplane Base/Water Landing Site Markings and Lighting (AMES, ASES)
Task F: Pre-Takeoff Checks
III. Takeoff and Departure Phase
Task A: Normal and Crosswind Takeoff
Task B: Glassy Water Takeoff and Climb (AMES/ASES)
Task C: Rough Water Takeoff and Climb (AMES/ASES)
Task D: Confined-Area Takeoff and Climb (AMES/ASES)
Task E: Instrument Takeoff
Task F: Powerplant Failure during Takeoff
Task G: Rejected Takeoff
Task H: Departure Procedures
IV. Inflight Maneuvers
Task A: Steep Turns
Task B: Approaches to Stalls and Stall Recovery
Task C: Powerplant Failure—Multiengine Airplane
Task D: Powerplant Failure—Single–Engine Airplane
Task E: Specific Flight Characteristics
Task F: Recovery from Unusual Attitudes
V. Instrument Procedures
Task A: Standard Terminal Arrival/Flight Management System Procedures
Task B: Holding
Task C: Precision Approaches (PA)
Task D: Nonprecision Approaches (NPA)
Task E: Circling Approach
Task F: Missed Approach
VI. Landings and Approaches to Landings
Task A: Normal and Crosswind Approaches and Landings
Task B: Landing from a Precision Approach
Task C: Approach and Landing with (Simulated) Powerplant Failure—Multiengine Airplane
Task D: Landing From a Circling Approach
Task E: Rough Water Approach and Landing (AMES/ASES)
Task F: Glassy Water Approach And Landing (AMES/ASES)
Task G: Confined-Area Approach and Landing (AMES/ASES)
Task H: Rejected Landing
Task I: Landing from a No Flap or a Nonstandard Flap Approach
VII. Normal and Abnormal Procedures
Task A: Normal and Abnormal Procedures
VIII. Emergency Procedures
Task A: Emergency Procedures
IX. Postflight Procedures
Task A: After-Landing Procedures
Task B: Anchoring (AMES/ASES)
Task C: Docking and Mooring (AMES/ASES)
Task D: Beaching (AMES/ASES)
Task E: Ramping (AMES/ASES)
Task F: Parking and Securing