The Thompson Snares Survival Kit contains two small-game snares (00S-20 and 0S-30), tie-wire, and instructions.
This type of snare was first issued to US pilots during World War II, and continues to see wide use to this day. These are the right size for small game like squirrel, weasel, marten, grouse, rabbit, and woodchuck.
Snares and traps offer a big advantage vs active hunting. Active hunting burns a lot of calories, is somewhat risky, and means that you cannot spend your effort on other tasks. Every snare you set increases the odds that you will have food. And by setting snares, you free yourself for other tasks (constructing shelter, getting water, etc.). The advantage of a snare over a deadfall-style trap: you do not run the risk of rupturing the animal's bladder and intestines, fouling the meat and possibly poisoning yourself.