Is my phone using both WiFi and 4G?
Your phone is not using both WiFi and 4G, but the 4G radio stays on and stays in sync with the tower (if you move from a 4G to 3G area while still on WiFi, you'll see the icon change when it recognizes the tower swtich).

On my Droid Bionic (Verizon), I have a Tasker script that turns off Mobile Data when I'm connected to Work or home WiFi networks; my battery life is greatly extended with this setup, and the phone works as I expect (I'm told that MMS messages require the Mobile Data connection, but I rarely receive them, so I can't say if that's true; if so, it may be one reason the radio stays on by default).