The two terms are often erroneously used interchangeably.
Abstract – A concise summary of a legal document, e.g., abstract of judgment, abstract of title, etc. An abstract of title is a summary of the history of a piece of real estate, including previous owners and any encumbrances that affect the title to the property – so it is the closest equivalent to the Hebrew word נסח, which is obtained from the Tabu (the Land Registry).
Extract – An exact replica of a portion or section of a document that has been extracted from a larger document. Since a נסח contains the entire history of the property in question, it is best to use “abstract” for that.