Elephant's-foot is a houseplant more often sold in the United States as ponytail palm, named for its long, cascading leaves. The swollen trunk stores water, and the plant is not a true palm. Wild populations in Mexico are critically endangered.
Spineless yucca (Yucca gigantea) has shorter, more upright sword-shaped leaves. Elephant's-foot has much longer, narrower leaves that spill downward; its swollen base is clearest on older plants.
Why they get mixed upBoth are U.S. houseplants with a woody trunk and a tuft of leaves.