1990 corolla fan prob

As soon as I switch the ignition key to 'on' -without even starting the car, fan comes on. After starting, it stays on. It doesn't shut off until the key is switched to 'off' This happens when the car is cold and sitting all night or after it has been driven.

i think the cause is the cooling fan switch sensor is this the same as the ECT sensor with a different name?

i was also told to first check the fan fuse as a 'fail safe' prevents the fan from shutting off after fuse has blown.