No no! That's not how it works.
What you've got is a chromatic tuner. Unlike your friend's lousy tuner, which makes you tune to the four notes it's set for and use a button to tune down, yours will let you tune to any note. It will listen to what you play and tell you what note you're closest to (in the upper right of the display), and how close you are (with the needle). That means you don't have to mess around with telling it to tune down -- you just tune to the notes you want, and stop when it says you're in the right place.
The Hz setting serves a different purpose. You set it to whatever you want the A above middle C to be. All the other notes will move a little with it to stay in the correct relative positions. Normally that's 440, but occasionally people like to set it higher or lower. 99% to 100% of the time the people you're with will be using A=440, so you're pretty much always safe at that setting.