Assuming they are from the same bean, is there a significant difference between the two? How would it be best described?
Yes there is a significant difference between the two. I would put them at pretty close to opposite ends of the coffee spectrum.
French Press: Generally made with a coarse grind, longer steeping time. Result is a weaker (less concentrated) more typical American style coffee. This will likely be consumed in the same way as a typical filtered, drip coffee would.
Moka Pot: Made with a much finer grind. And while many will argue it's not true espresso. It is much closer to being an espresso. I don't really care what you call it, but it'll be a much stronger more robust coffee. The same amount of coffee will be extracted to a smaller quantity of water. This would be consumed in the same way as an espresso would. You can water it down to make an Americano, etc...