Hello Miguel;
I'm familiar with the terms:
Certified Material Test Report (CMTR) - actual test data, chemical and mechanical test results for a particular heat or lot for the material you received. The chemistry may be the ladle analysis or a product analysis. For wrought material, the mechanical test data is for the material you received.
and
Certificate of Conformance (C of C) - a letter stating the material meets the requirements of the specification. The data listed are simply typical ranges for the specific elements and mechanical test results, but the data is not specific to the material you received.
The two terms you mentioned are new to me. Can you give us some context?
Al