The potato-like starch that you find in Latino cuisines and in some trendy bistros nowadays is cassava or Manihot esculenta, a native of South America and consumed in large quantities throughout Latin America, Africa, South Asia and the Caribbean. Yuca – pronounced yoo-cuh - is the root portion of the plant. Tapioca flour and pearls are made from the powdered root, along with many other common foods - check out this Wikipedia article for just a few of the hundreds of uses for cassava.
Yucca, on the other hand, is an ornamental plant:
They are those spiky flowered plants common in Southern and Western parts of the US, including Florida, New Mexico, and California. But they don't have the edible root of the yuca, and are commonly confused.
From Wikipedia: "Yuccas are widely grown as ornamental plants in gardens. Many yuccas also bear edible parts, including fruits, seeds, flowers, flowering stems, and more rarely roots, but use of these is sufficiently limited that references to yucca as food more often than not stem from confusion with the similarly spelled but botanically unrelated yuca."
Oops. Someone should probably let the restaurant know...
(Image credit: Wikipedia)