Toyota's marketers apparently got a little over-infatuated with the name of their most successful car during the early-to-mid 1980s, and so North Americans had a bewildering array of vehicles with Corolla nameplates. In this case, we've got a front-wheel-drive Tercel with Corolla badging, which was sold side-by-side with rear-wheel-drive E70 Corollas in the Toyota showrooms. Bigger and more expensive than the Starlet, but still cheaper and more economical than its big Corolla brother, the Corolla Tercel sold pretty well.
I found this car down on the beach, not far from the surfer '59 VW Transporter and the '73 Volvo 1800ES. Since this is the Bay and the "surf" is about 6" at its most raging, there's no danger of salt-spray corrosion.