In the jackknife, you compute some statistic of interest in each subset of the data. The average of these subset statistics is compared with the corresponding statistic computed from the entire sample in order to estimate the bias of the latter. You can also get a jackknife estimate of the standard error of a statistic. A value of 10 for k is popular for estimating generalization error. SBC provides consistent subset-selection, while AIC does not.
Noise variance is the same for all subsets of inputs.
In the simplest form of bootstrapping, instead of repeatedly analyzing subsets of the data, you repeatedly analyze subsamples of the data. Each subsample is a random sample with replacement from the full sample. Depending on what you want to do, anywhere from 50 to 2000 subsamples might be used. Dijkstra, T.K., ed. Morgan Kaufman, pp.