They appear functionally similar, but the coffee made is very different. A standard french press requires a coarse grind and you can only adjust extraction by changing the steep time. The Aeropress pushes coffee through a paper filter with an airtight seal. You can vary both grind size and steep time. Not only that, but you can vary extraction across the brew by very slowly pushing the coffee through the filter. (This is a very important feature of pressurized brewing methods such as espresso.)

These controls allow you not only to better tune for different beans, but to successfully make different styles of brew for a single type of coffee. (For instance, you can adjust those variables to successfully make a shorter, more espresso-like brew or a taller, more pour-over like one from the same coffee beans.)