Do canon eos 20d and canon rebel 2000 have the same lens mount?

Yes, both of them are EF Mount .

Awesome. I wanted a second opinion.  

*NO* 20D has the EF-s mount, while the film camera has the EF mount.

That lens will mount find on both cameras, but the 20D has the EF-s mount, not the EF.

Now, a lens that mounts on the film camera will mount on the EF-s mount with absolutely no issues.
An EF-s lens will not mount though on an EF camera.

The sigma will mount just find on the 20D as that camera can take any lens whether it is EF or EF-s. (It will also mount fine on the full frame camera)

Damn my grammar. I meant "fine" not "find"
How long till i'm able to edit my comments?  

Yes, Username you are right. please check the canon website for the details.
http://www.usa.canon.com/cusa/support/consumer/eos_slr_...

I copy it here " Compatible with not only Canon's new EF-S Lenses, but with the entire EOS System of lenses and flashes "

I have been used it for the backup camera for many years.

If the lens is for Rebel 2000 then it can use it on EOS20D.

Now, a lens that mounts on the film camera will mount on the EF-s mount with absolutely no issues.
An EF-s lens will not mount though on an EF camera.