What is the difference of EF and EF-S?!

I have had a rebel all of my life and now finally moving on up to a 60D. I was introduced to full frame cameras while shopping and was totally lost but figured I didn't need to spend the money since it is still a hobby of mine and not really making money off of my photos. But I can not figure out exactly the specifics behind what the difference in a EF and EF-S mount lens is...?

I am confused by the conversion of the lenses, if I was to buy a 10-20mm EF lens and put it on my 60D it would equal to 16-32mm?

But if I bought a 10-20mm EF-S lens that would be just 10-20mm...? But, I cannot use an EF-S lens if I do decide to move to full frame cameras like the future of photography looks to hold.

Also, is a 10-20mm EF lens on a full frame camera then just 10-20mm?

Someone please help in this explaining this because I cannot find anything on it and I am always hearing different things!