What is the difference between nuclear fission and nuclear fusion?
Nuclear fission involves the splitting of a heavy nucleus into two lighter fragments plus the release of energy.  As an example here is one route by which $\ce{^235U}$, a fissile material, can split apart.

$$\ce{^{235}_{92}U + ^{1}_{0}n -&gt; ^{141}_{56}Ba + ^{92}_{36}Kr + 3^{1}_{0}n + 200 MeV}$$

Note the 3 neutrons generated in the fission process, they are part of the chain reaction; they allow the reaction to propagate at an even faster rate as they go on to react with 3 other $\ce{^{235}_{92}U}$ nuclei.

Nuclear fusion involves the fusing together of nuclei to form a heavier element.  Again, energy is released in the process.  Here is an example of a fusion reaction involving the combination of 2 deuterium nuclei.

$$\ce{^{2}_{1}H + ^{2}_{1}H -&gt; ^{4}_{2}He + ^{1}_{0}n + 17$.$6 MeV}$$