An individual's heritage describes their lineage. Who their ancestors were, where their ancestors came from, what the lives of their ancestors were like, how the lives of their ancetors led to where the individual is today, etc. Folklore is an example of cultural heritage.
An individual's culture describes the social climate and traditions in which they were raised. This can include cultural heritage in the form of beliefs and traditions, but what distinguishes culture from heritage is that culture decribes the now whereas heritage describes the then. A whole variety of elements are included in a person's culture from langauge to religion to recreation to gender roles.