They are not the same thing but they are related.
MTHFR is a genetic snp that is responsible for taking all the folate you eat and turning it into methylfolate. Methylfolate is important for the Methionine cycle. The Methionine (Methylation) cycle takes homocysteine, converts it into methionine (using several co-nutrients) which then makes SAM. SAM is a potent methyl donor that helps methylate things such as your estrogen in phase 2 detoxification. Once SAM donates its methyl group, it returns to the cycle as SAH and the process starts over again.
If someone has a "dirty" MTHFR (as referenced by Dr. Ben Lynch's book, Dirty Genes, that I highly recommend) you will have methylation problems with things ALL OVER your whole body, not just with folate.
Let's take estrogen as an example. When your body is done with your two main estrogens (E1 and E2), it pushes them into phase 1 detoxification and they are known as the metabolites, 2-OH or 4-OH. Typically, 2-OH is the preferred pathway while the 4-OH pathway is considered the 'naughty' pathway if it does not get methylated because of its risk for causing DNA mutations. During methylation, the 2-OH and 4-OH get turned into 2-methoxy and 4-methoxy.
While MTHFR is important for the Methionine/Methylation cycle, it's actually the creation of SAM that is so important for estrogen. A different enzyme made by the COMT snp uses SAM to detox estrogen. Therefore, your estrogen detox relies on both MTHFR and COMT.
If you have a broken MTHFR (or COMT), there is a much higher chance that you could have estrogen detoxification issues. This may be the cause of your PMS, heavy periods, clots, tender breasts, and moodiness. It may also increase your risk for estrogen based cancers.
Does this mean you should take methylfolate if you have mutations in your MTHFR gene? Not necessarily. It depends on a whole lot of other factors and symptoms. Work with your functional health care practitioner to guide you appropriately!