Can someone fill me in on the different yo-yo response types? I know some of them by name, but is there any difference between, say, an o-ring response and a silicone response? Or a K-pad and a friction sticker? Like I said, I know their names, but I have no clue which one’s which if they’re lined up in front of me. (Except maybe for a few) :-[

This video knocks down some of the basic stuff.

Lets go more in depth. There are many types of response. Here are some of the most basic ones:
    -Starburst
    -O-Ring
    -Pads
    -Silicone
There are more response types, but those are the basic ones.

Anyway, i’m going to answer your initial questions. The most basic difference between an O-Ring and Silicone, is material. O-Rings are made out of rubber, while silicone is just silicone. Also, silicone tends to be more unresponsive with grippier binds.

K-Pads and Friction Stickers have pretty much the same differences. K-Pads are silicone, and Friction stickers are stickers coated in rubber.
Here is a picture of many response types:

Top row from left to right:
  Duncan friction sticker • YYJam Matrixx O-ring • ProYo brake pad
Bottom row from left to right:
  Henrys Tiger Snake raised ring • Losi star burst • ProYo GT wood