Module means, as defined in the KEGG Module page, a functional unit. So it can be anything, from groups of enzymes to genes to metabolites. About the two that concerns you:
Pathway modules represent groups of functionally related enzymes part of the metabolic network. I think this one is easy to understand because it represents the classical understanding of "module". The modules involve metabolites (compounds with id starting with "C"), enzymes (represented by KEGG ortholog ids starting with "K") and reactions (represented by ids starting with "R"). The reactions integrate compounds and enzymes in a particular step in the chain of reactions included in that module.
Signature modules represent molecules associated with a particular phenotype. In particular, the example listed in the KEGG page points to EHEC pathogenicity signature, Shiga toxin. The two molecules in module M00363 are associated with the phenotype, which is in this case EHEC pathogenicity. But in principle they do not necessarily need to be related to each other (in this case they are, but not in the same meaning as the metabolic module).
In your particular examples, M00115 is again a pathway module including enzymes, compounds and reactions, all connected in an integrated manner. Module M00542 on the other hand shows the proteins part of the T3SS (Type three secretion system) used by Gram-negative bacteria for infection. These are not enzymatic reactions, just proteins associated with the EHEC/EPEC pathogenicity phenotype. They are however related in that they form a protein interaction complex that mediates infection.
Other Module categories include:
- Structure complexes related to molecular machineries.
- Functional sets seems like a miscellaneous category.
You could argue that the T3SS is a molecular machine and should be classified in the Structural complexes category. Indeed, something important to remember is, as stated in the KEGG module's page:
KEGG MODULE is a collection of manually defined functional units [...]
As anything manually defined, there is some degree of arbitrariness. Use the information in KEGG modules as far as it serves your needs, but it would be better not take it as written in stone.
M00115 is a pathway module (NAD biosynthesis) whereas M00542 is a signature module (EHEC/EPEC pathogenicity signature).
From the KEGG page on modules:
pathway modules – representing tight functional units in KEGG metabolic pathway maps, such as M00002 (Glycolysis, core module involving three-carbon compounds)
signature modules – as markers of phenotypes, such as M00363 (EHEC pathogenicity signature, Shiga toxin)