Do they make special kinds of DVD and Blu-ray discs made out of metal like aluminum and steel?

All are made of metal and plastic.

The plastic: because they need to be transparent on one side (or both, depending on the disc type) so that the player can read the data contained inside the disc.

https://electronics.howstuffworks.com/dvd2.htm#:~:...

The metal: for a DVD is typically aluminum AND gold.

CDs were aluminum, and when they first became popular some companies were selling special, high-end gold instead of aluminum, claiming some advantage or other. I don't think it sold well, considering that the regular (aluminum) CD produced equally good sound quality.

It is impractical to make them with pure metal, because all of them already contain a very thin layer of aluminum under the protected plastic coating. 

They used gold to make special one, don't know about aluminum and steel. DVD are already history.