Hey! Familiarity is BEING familiar with something, familiarization is BECOMING familiar with something. Does that help?

In this context, the difference in meanings is that the first sentence tells us that she was already familiar with the language which helped her whereas the second sentence says that even though she didn't know the language, she has been trying to grow familiar to it and as a result she has achieved enough familiarization to allow her to enjoy her stay. e.g. Since she is a native of Spain, her familiarity with the Spanish language helped her enjoy her stay in Mexico ! Since I have been learning Spanish for quite some time now, my familiarization with the language has helped me enjoy my stay in Mexico :)