The process of RNA interference (RNAi) can be moderated by either siRNA or miRNA, but there are subtle differences between the two. Both are processed inside the cell by the enzyme called Dicer and incorporated into a complex called RISC. siRNA, however, is considered exogenous double-stranded RNA that is taken up by cells, or enters via vectors like viruses, while miRNA is single stranded and comes from endogenous (made inside the cell) non-coding RNA, found within the introns of larger RNA molecules.
Another difference is that, in animals, siRNA typically binds perfectly to its mRNA target, a perfect match to the sequence, whereas miRNA can inhibit translation of many different mRNA sequences because its pairing is imperfect. In plants, miRNA tends to have a more perfectly complimentary sequence which induces mRNA cleavage as opposed to just repression of translation.
Both siRNA and miRNA can play a role in epigenetics through a process called RNA-induced transcriptional silencing (RITS). Likewise, both are important targets for therapeutic use, because of the roles they play in the controlling gene expression.