Ziziphus, jujube, and date all refer to types of dates in a broad sense, but in non-professional contexts, "jujube" may be used generically to refer to the fruits of all Ziziphus genus plants. However, strictly speaking, these three terms are not equivalent.
Ziziphus is a genus name of plants belonging to the Rhamnaceae (buckthorn) family.
Jujube refers to the Chinese date, date tree, red date, or Ziziphus jujuba. It is a species within the Ziziphus genus of the Rhamnaceae family and is often used as a general term for "date," but strictly speaking, it specifically refers to Ziziphus jujuba.
Date also refers to a type of date, a term derived from the Greek word via Old French, representing dates that are as long as fingers, primarily produced in the Middle East, and specifically refers to the date palm (Phoenix dactylifera), though in some contexts the term may be colloquially used for jujube as well, but with the distinction noted above.
Ziziphus is the genus name, and jujube is a specific species within that genus.

We are a manufacturer of organic Ziziphus jujuba extract. Our raw materials come from USDA/EU organic-certified farms, with no pesticides or chemical fertilizers used. We use 0-pesticide, 0-heavy metal Xinjiang Ruoqiang organic red dates for production. These dates grow in areas with large temperature differences between day and night and in unpolluted environments, resulting in a 30% increase in extracted saponin content. If you would like to learn more about our products, please feel free to contact us at any time.