Trailing Jade and Jade Plant look like they're closely related (except for that part about how one's trailing and the other isn't), but they're actually in separate families. And from different parts of Africa. Jade Plants are native to South Africa but Trailing Jade is from farther north and east, in the area of Tanzania. They are also succulents, and so need sun and not too much water.
Phylum/division: Magnoliophyta
Class: Magnoliopsida
Order: Asterales (an order containing many plants that seem nothing like trailing jade - e.g. sunflowers and daisies)
Family: Asteraceae
Genus: Senecio (even at this level there are both succulents and non-succulents, which I found surprising)
Species: S. jacobsenii