No. AP ships with all cars. It is TACC+lane keeping drivers assist.
EAP is a $6,000 option that gives you the ability to do enable auto lane change with NoA, Summon, Smart Summon, and Autopark...basically lane change is the only valuable addition there.
FSD gives you what EAP does plus, Traffic Light and Stop Sign Control, basically can stop at lights/stop signs. Driving on City Streets is coming soon to the regular FSD stack, but you have the option to enter FSD Beta, if you qualify and are accepted, which allows the car to "autosteer on city streets".