What is the diffrence between DRC and DFM ?

DRC - Design Rule Check

This is specified by the technology and foundrys all over the world give out these
rules for a particular technology. These rules have to be satisfied in any design (physically)

DFM - Design For Manufacturing

Its a thing which has been there since the 90nm node. As yield and reliability became important factors, foundrys brought out the DFM, which is making designs reliable and yield high.
These are set of rules , we would say guidelines that cover over the DRC rules. These rules are optional but as we go down the deep submicron technologies, its highly important to follow these DFM rules in order to make sure the product is reliable and yield is maintained high.
Making a design with DRC rules has a high probability that the yield of the design is quite less...
Foundrys specifically recommend all the design companies to follow DFM rules wherever possible... 

It is very important of following points:
Yield
Performance 
and
life time of chip.

DFM is very big issue in VLSI.