Do smaller wings mean faster flight?
On the whole, smaller wings produce less drag, but they also produce less lift. Less drag means the same engine can reach a faster cruise speed, but less lift limits the weight capacity and means the aircraft needs to go faster to stay airborne: the stall speed, take-off speed, and landing speed will all be faster, which in turn means longer runways are needed (or systems like catapults and landing chutes).

For a fighter aircraft, that top speed matters a lot more than the lifting capacity or take-off speed, so they're optimised with these low-drag, high-lift wings. Compare to a utility aircraft of the same size: the utility aircraft will have a less powerful engine, and wings that produce more lift at lower speeds. A utility aircraft that needed the same kind of runway as a fighter would be pretty useless.

In the other direction, compare to an airliner. These wings are tuned like a fighter's: to be maximally efficient in the cruise. But the airliner has to lift a lot more weight, so the whole aircraft is much larger, and the wings are in proportion to that. They typically also require long runways, and fly faster than a small utility aircraft. But look at the Hercules military transport. It's designed to lift a lot, but it also needs to operate from poor-condition, short runways. It has less efficient, high-lift wings, so its take-off speed is very slow for its size, and it isn't that fast in the cruise.

In summary, wings (not just wingspan, but also the shape of the wing) allow you to trade off lift and drag. High lift and drag gives you slower take-off and landing speeds, but you pay for that with a less efficient cruise. Low lift and drag gives you a faster cruise, but you pay for that with ridiculous take-off and landing speeds and the extra runway that requires.