It's not clear whether Tesla has a local map. They've never shown pictures of one, unlike Google. The Mobileye unit definitely does not; you can buy a Mobileye aftermarket unit and watch it put rectangles around things that look like cars and people. Tesla's radar probably just returns targets and range, like most first-generation automotive radars. Tesla's system may be entirely reactive.

Google builds maps; they do path planning, so they have to.