Essentially the difference is partially to do with the source of the RNA interference (RNAi), and partly down to the structure of the final molecules. Sort interfering RNA (siRNA) is exogenous (originates from outside of the cell), whereas micro RNA (miRNA) is endogenous (originates from within the cell.) Both siRNA and miRNA are non-coding and are primarily targeted at gene repression.
As miRNA are endogenous they are produced through protein/RNA interaction within the cell expression them.
They can be told apart as siRNA molecules exist in a duplex, whereas miRNA are single stranded. They can be further told apart through sequencing, miRNA tend to be less specific than siRNA being only partially complimentary to the RNA being knocked down.