Are there different pins for USB 3.0 and USB 2.0 Ports?
Yes. USB2 ports only have four pins, whereas USB3 ports have nine. The physical plug on the computer is the same, so a USB3 device will work on a USB2 port and vice versa. However, the header to the motherboard is entirely different. If the chassis you buy only has USB2 ports on the front, you will need an adapter to wire them to the motherboard. You will not be able to get USB3 speeds out of those ports no matter what you do. There are plenty of small form-factor cases that have USB3 on them so I would just recommend shopping around some more if it's that important to you.
So, does my machine have some USB 2.0 ports and some USB 3.0? How can I identify them?
If your motherboard has USB3 support, then at least some of the ports on the back of the motherboard will be USB3. USB3 ports are usually color-coded in blue whereas the USB2 ports will usually be black. This isn't a standard rule, though, so this might not be true on your model. You'll need to consult the motherboard manual to see which ones are which.