Can anyone tell me the difference between a Heavy Duty Toggle Switch and a Medium Duty Toggle Switch? What is meant by these terms?
For a FIRST team, the difference is minimal for an operator interface. The differece between the two may be either a one-million stroke warrenty or a ten-million stroke warrenty. Either way, you are never going to approach that kind of numbers in only one season, even if you have to hit fire every time you fire a Poof ball.
We used some of these medium-duty toggle switched for our OI in 2004, and they worked fine. The push buttons we used on our 2005 OI were rated at 10,000,000 cycles, and they held up fine.
Just make sure the buttons are BIG and easy to hit! Using little tiny toggle switches may seem like a good idea, but can lead to a poor design choice. Especially if you have a few near each other, the driver has to look down during the match to find the right one. This detracts from the time the drivers have to actually get the robot from point A to point B and score. As the operator / co-driver for my team last year, I cannot stress how much easier it is for the drivers to have big buttons. 
EDIT: If possible, try to find replacement buttons for arcade machines. We’ve had good luck with Happ Controls with my team. Besides being really cool, these buttons were designed with rough play and long life in mind. 
mechanically a heavy duty switch is designed to be switched thousands, or tens of thousands of times, and mounted someplace where it might see lots of rough handling
less expensive switches are used for things that dont get turned on and off that often.
Also pay attention to the contact current ratings. If they are referring to the current a heavy duty switch will handle more.
A medium or light duty switch would be ok for your operator interface control box. If you are going to put switches on your robot (to select different auton modes for example) they should be heavy duty switches if there is ANY chance they will get bashed during a match.
What about solder or screw connections? Which do you think is better? On one hand I don’t feel like soldering them, but then it’s a better connection. Will it really matter whether I use screw or solder terminals?
Cronos,
As to heavy, medium and light duty switches, some manufacturers actually use the same internals for all of their designs while strapping a different handle for each different application. There is no difference between solder and screw other than the weight (screw adding more) when properly terminated. The solder gives an extra measure of reliability/comfort.
Something to remember is that all switches have switch bounce, a little noise right after the switch makes contact. Know that it occurs and have your programmers compensate so that a noisey switch doesn’t get the robot into trouble.
Ive noticed over the years that students sometimes tend to be a little sheepish tightening fastener (screws, bolts, nuts…).
If you use screws make sure someone secures them snugly, and a star washer is your best friend.
one problem with screw terminals on things like switches: if the wire will be pulled side to side the leverage on the wire can loosen the screw. If you use screws make sure the wire it tiewrapped downstream so it cant wiggle on the back of the switch.
not our team… many snapperd bolt heads, stripped screws, crushed pieces etc. we need a torque wrench.