When running MRP using transaction MD02 and MD41, what the difference should be?

There is no difference in the processing logic as such. The only difference is that MPS only acts on materials with an MRP type relevant to MPS (e.g. M0, M1, etc...), and MRP acts on materials with an MRP type relevant to MRP (e.g. PD). How the materials are processed is exactly the same.

This functionality allows you to run MRP for 2 sets of materials separately (and with a different frequency).

For example, some businesses may do planning for their finished goods once per week, but would want to run MRP for their
components daily (although this is generally not necessary with SAP).  So, for this example, you would define all finished goods with an MRP type relevant for MPS, and all components with an MRP relevant.

Basically, MPS is a form of MRP that concentrates planning on parts or products that greatly influence the company profits or those that require critical resources.  Items marked as master schedule items can be finished goods, assemblies or raw materials.  These items are selected for separate MPS run that takes place before the MRP planning run.  MPS run is executed without any BOM explosion.  This is to allow the MRP controller to ensure that the master schedule items are correctly planned before any detailed MRP run take place.

By Arturo Senosain :

As you can see, there are not too differences if you review MRP and MPS isolated, but lets think the BIG PICTURE, and can find the difference is just an procedure stuff:

1: RUN MPS (tcode: MD40). SAP do the planning run multilevel, also considering the  MRP materials.

2: Do the the necesary MANUAL changes in your MPS materials Planned Orders, remember that the planning run is  "JUST AN ADVICE" and never can replace the human decision. Here, you have your MPS Plan, and also the consumtion Plan (dependant requirements)

3: Then, with the dependant requirements OK (acording to MPS's Materials Planned Orders), do MRP RUN (tcode: MD01). The MRP run dont change the MPS plan.

The idea of MPS and MRP is to "separate" materials, in order you can run "masive process" in order. The algorith of mps and mrp are the same. Both work with the PlanTime Fences and Fixation types, rescheduling is the same,  and so on.

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