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So is a dsl modem in fact a gateway? >>
Sort of. An EXTERNAL would be considered a gateway, an internal would not; except that since an internal does let you get on the web, it could slightly be considered to be one.
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What is the/is there a difference between a gateway and a router? >>
For your purposes, none. In reality, though, the consumer/SOHO units that everyone calls routers are simple gateways. A real router is a more complicated and robust device used in larger networks.
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I am wondering if I can just use an el cheapo router to set up el cheapo dsl service at home and avoid having to rent one from the provider. >>
It is nearly impossible to buy a DSL modem anywhere but the ISP. I think Intel makes one, but it may, or may not, be compatible with your providers setup. You can also pick them up used sometimes.
Your question indicates that you may be confusing the DSL modem with the routers, such as the Linksys and Netgear. They are not the same thing.
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Do most providers insist you use their equipment? >>
They'll tell you that, but you don't have to. Problem is a) finding the equipment that will work with them, and b) forget about tech support.
Here is a sample diagram to illustrate a typical setup. (Word Doc, 60K)
Russ, NCNE