According to the Umass Amherst Center, heritage is defined as the "full range of our inherited traditions" which includes things like language, literature, style of dress, songs, and buildings. Heritage is not just about preserving old things. In fact, heritage includes ideas and memories, too. So, it is about preserving our shared past rather than just keeping specific items.
In contrast, according to Texas A&M University, culture has many different definitions. For some, culture refers to the "way of life" of a particular group of people. But it might also refer to the behaviors learned through socialization or the shared knowledge and experiences of a particular group in society.
So, there is a key distinction to remember between these two concepts: heritage refers to the things that we inherit, while culture is about what we create.