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Goodness of fit test is used to test a single population. The null hypothesis will be that the observed frequencies are equal to expected frequencies (based on computed intrinsic values given the extrinsic values).

A good example would be comparing observed phenotype frequencies against expected frequencies calculated from the parental genotypes (Simple dominance gives rise to 1:2:1 ratio with two parental heterozygotes).

Contingency test is used to see whether or not different populations are associated. The null hypothesis will be that that different populations are independent of one another.

A good example would be comparing the effect of different host plants on different populations of insects. (Effect of Host A on Insect population 1, 2, 3; Effect of Host B on Insect population 1, 2, 3; etc)

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