How is the same takeoff performance achieved by a specific engine type on aircraft of different sizes?
There are several model variations of that type engine.

Refer to the Type Certificate Data Sheet (TCDS) for the Boeing 737.  You will find listed the specific model number numbers and thrust for each approved engine.

For example, here are the CFM engine models approved for specific model/serial numbers of the 737.  You will have to get the latest revision of the TCDS for new models, like the 737 MAX.  This excerpt from the 737 TCDS shows the model variety of one type engine (the CFM56-7B) as approved for certain 737s: