Difference between KEGG Pathway and Module (from KO mapping)
A pathway shows all the reactions required for the synthesis / metabolism of a given product.  A module is a functional unit that can be utilized in a pathway, and some modules are common to many pathways.  For example, look at the tetracycline biosynthesis pathway 00253.  This pathway has a description at the top that includes this excerpt:


  Tetracyclines contain a linear tetracyclic skeleton, which is formed from a malonamate starter unit and malonyl-CoA extender units through a common polyketide pathway [MD:M00778].


Confusingly, that "common polyketide pathway" is actually a module, Type II polyketide backbone biosynthesis, acyl-CoA + malonyl-CoA => polyketide or M00778.

Note that this module is included in other pathways:


  map01056 map00253 map01100 map01130 


Looking at the drop down menu at the bottom of the module page, we see that the Reference Module contains multiple different KEGG Orthologs that perform the same function in different systems.  

  

Choosing an organism from the drop down menu, the specific Orthologs used by that species are highlighted.  



So, you can see how separating pathways into modules can help in identification of these components in other organisms, even if the full pathway does not exist.