a leather strap that attaches to the saddle...that prevents the saddle from sliding forward...know what it's called?

That's called the cinch.

...isn 't it?

For more information than we are likely ever to need about saddles, take a look at
http://www.rrvfsbo.com/articles/wessadpts.htm .
And that's just for western saddles. There's apparently an English saddle, too, which is a horse of another color entirely.