Subdomain pointing

How can I could I make it so that a subdomain points to a subdirectory on my website, and treats that subdirectory as root for that subdomain. For example:

www.mysite.com/subdir = subdomain.mysite.com/

And is there a way to point a subdomain to do the same thing but use an entirely different site?

subdomain.mysite.com = www.anothersite.com/

So that browsing the subdomain would appear the same as browsing the other site URL.

 

 

 

 

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