[Coda]

You're not wrong to find the two concepts confusing. They're measured in the same units, and they measure different aspects of the same thing.

The short version is that energy is the ability to do work. In order to do X joules of work, you have to have X joules of energy. Kinetic energy is always positive. (You can see this in the math -- the velocity is squared, which means if you had a negative velocity it would still end up as a positive answer.)

Conversely, work is a measurement of how much energy is transferred. It represents a net change in kinetic energy. Saying "final" kinetic energy is only true if the initial kinetic energy was zero. It could have already been moving and ended up moving faster, or it could have been slowing down instead of speeding up (though in that case, the work is negative, which means the force was applied in the opposite direction of motion; equivalently, it means that energy was taken away).

The reason you have to say "net work" is because you might be dealing with multiple forces. For example, if there's a box sitting on the floor, and you push it, you did positive work on the box, because you applied a force over a distance. But the box isn't moving at the end, so its kinetic energy before and after is zero, so the net work must also be zero. The resolution to this is that friction was performing negative work on the box -- an opposite force over the same amount of time.