I always thought it was, 'he who laughs last, laughs loudest' but my SO insists it is definitely, 'he who laughs last, laughs loudest'. As to it's meaning, I'm with Bingley.
**incidentally** here's http://www.calvin.edu/~lhaarsma/maxims.html a muted chuckle.

those googlesults in full
he who laughs last, laughs loudest 231
he who laughs last, laughs longest 303
he who laughs first, laughs loudest 0
he who laughs first, laughs longest 0
he who laughs first laughs last 78
he who laughs first laughs best 1
he who laughs first cries at the last 0

from Cambridge Int.
maxim
noun [C]
a brief statement of a general truth, principle or rule for behaviour
adage
noun [C]
a wise saying; proverb: (from Latin i fink, means saying)
proverb
noun
a short pithy saying in frequent and widespread use expressing a basic truth or practical concept.
aphorism
noun [C]
a short clever saying which is intended to express a general truth.

so, not much difference really. a maxim is more like a rule. proverb and adage really are the same thing. an aphorism seems to me to be more likely to be a direct quote, and doesn't have to be in widespread use.