The two techniques are closely related so much that each is considered as a variant of the other. Bootstrap involves resampling with replacement and therefore each time produces a different sample and therefore different results. Jackknife on the other produces the same result. It is used to assess bias and variance. Bootstrap application is more cumbersome than that of the jackknife. With computer facility it is the more popular.
When your sample size is small and you don't know distribution of your data, you can use both bootstrap and jacknife methods to assess bias and variance of your supposed statistics. In addition, you can calculate confidence interval or test a hypothesis about your supposed statistic without knowing distribution of your supposed statistic. I usually prefer using bootstrap instead of jacknife.
Bootstrap and Jackknife are methods used to estimate bias and standard error; and the mechanisms of both resampling methods are not big different: sampling with replacement vs. leave out one observation at a time.
Application of bootstrap is more cumbersome than that of the jacknife. you can calculate confidence interval or test a hypothesis about your supposed statistic without knowing distribution of your supposed statistic by using bootstrap.
Sir, in case of Jackknife, we can gate a fixed set of resample (pseudo sample). Let say, we have a sample of size n, we can get (n-1) pseudo-samples by deleting one observation at a time.
whereas in case of Boostrap, it is not the case of Jackknife, we can get as many as up to n to the power n numbers of pseudo-sample if we consider with-replacement.