What causes the different types of tire skidding noises?
The screeching that you describe is unlikely to be caused by the tyre skidding. It's more likely to be the contact between the brake pad and the braking surface causing the sound. 

On an alloy-wheeled rim-brake setup, this is the rubber pad rubbing on the rim. If it's squealing, then it could mean that the surface of the pads has picked up some shards of the brake track and is scraping them on the brake track. 

On a carbon-wheeled rim-brake setup, this could just be the standard sound. Some carbon wheels are just loud under braking and there's nothing to be done. 

On a disc-brake setup, this could indicate that the pads are contaminated, requiring replacement. If the pads are sintered, then like the carbon wheels with rim-brakes, there's only so much you can do. Sintered pads are just known to be a bit noisier. 

In any of these types, worn-out brake pads can also cause a screeching sound. If this is the cause, then you just need to replace the brake pads.