What is the difference between Hypothesis Testing and Classification?

Neymann-Pearson Paradigm

Multiple Hypothesis Testing

Multiple Testing Problem

FWER Control

The family-wise error rate (FWER) is the probability of falsely rejecting at least one true null hypothesis,

A procedure controls FWER at level $\alpha$ if $\PP(V\geq 1)\leq \alpha$, regardess of the number of true null hypothesis $n_0$.

FDR Control