* Heritage language: This refers to a language learned at home or in the community, often from parents or grandparents, but not necessarily the official language of the wider society. It's usually associated with immigrant communities or multilingual families.
* Home language: This simply refers to the language primarily spoken at home. It could be the same as the official language of the country or region, or it could be a different language.
* First language: This is the language a person learned first and is usually the most fluent in. It's also known as the native language or mother tongue.
If you could provide more context about where you encountered the term "hearth language," I might be able to give you a more specific answer.