Yes, AMD chips run at a slower speed. I have a AMD Athlon 64 3200+ processor on my computer. The processor actually runs at 2.0GHz, but the 3200+ specifies that the system has the equivilent processing power of a 3200MHz (3.2GHz) computer.
This is why many gamers like using AMD processors because they run cooler then their Pentium 4 equivilent.
I've see an AMD K6 running at no more than 4-500 MHz run nearly even with my 2.2 P4 in my laptop. It's pretty impressive to see in action, and I wouldn't have believed it if I hadn't tried it myself. The K6 had not much less RAM than the laptop did.
You can't really go by the Gigahertz number anymore. The reason for this is that some processors have a lower number of pipelines than other processors. Pipelines essentially break larger instructions down to smaller instructions. A processor with more pipelines will have to run at a higher clock speed (measured in GHz) than a processor with less pipelines. For example, an Athlon XP with a 10-stage pipeline, and running at 2.0Ghz is as fast as a P4 2.4Ghz with a 20-pipeline. Since most people look at the Ghz number to determine speed, AMD started including the comparative GHz number in their names (Athlon XP 3200+ is comparable to a 3.2Ghz P4 Processor).
Now, keep in mind that Intel is moving away from using GHz as a determining speed factor as well. Intel's Core 2 Duo is pretty much the dominating processor in the market right now and runs in the 1.82Ghz to 2.8Ghz range.