The starter relay (solenoid) points are melted together.
why would my starter wire burn, going from starter to battery
No. A bad starter would cause the car not to start.
If your motor is actually starting and not just turning over because the starter is forcing it to then I would check out your ignition switch to make sure your getting power to all the right things in the "Run" position as well as the "start" position.
You need to replace the starter.
The starter itself.. that would be unlikely... but a wire connected to the starter could on some vehicles.
The starter is probably not aligned with the flywheel. The clearance between the starter and the ring gear needs to be checked.
bad starter or starter solenoid.
Starter selenoid no good
bad starter or bad connection to starter or bad ground on battery or starter
It might happen because of a faulty starter gasket.
if it is in fact the starter, it is probably engaging the flywheel. starter may be faulty.
the bendix gear on the starter is stuck on the flywheel remove starter check bendix gear for wear if worn to bad replace starter