They are applicable in different circumstances.
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It depends on the population.Use t-test for a small population, N < 30; otherwiase, apply z-test or when N>=30.
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In a general t-test, there is no relationship between the members of one sample and the other. In a paired t-test they are connected in some way so that they are likely to give similar outcomes. This means that more of the difference between them can be attributed to the "treatment".
t test is used when- a) variables are studied b)the size of sample is a small one.(n<30) chi square test is studied when a) attributes are studied