Conditinal Random Fields (CRFs) are a special case of Markov Random Fields (MRFs).
1.5.4 Conditional Random Field
A Conditional Random Field (CRF) is a form of MRF that defines a posterior for variables x given data z, as with the hidden MRF above. Unlike the hidden MRF, however, the factorization into the data distribution P (x|z) and the prior P (x) is not made explicit [288]. This allows complex dependencies of x on z to be written directly in the posterior distribution, without the factorization being made explicit. (Given P (x|z), such factorizations always exist, however—infinitely many of them, in fact—so there is no suggestion that the CRF is more general than the hidden MRF, only that it may be more convenient to deal with.)
Source: Blake, Kohli and Rother: Markov random fields for vision and image processing. 2011.