siRNA's and microRNA's?

The difference is in their origins.  

MiRNAs are transcribed like other RNAs.  The pricursor (pri-miRNA) forms a stem-loop secondary structure that is recognized by the microprocessor complex composed of DGCR8 and Drosha.  Drosha is an RNase III class enzyme that cleaves the stem-loop out from the pri-cursor to form the hairpin shaped precursor (pre-miRNA).  Pre-miRNA is exported from the nucleus to the cytosol by exportin5 and Ran-GTP. In the cytosol, another enzyme complex made up of Dicer and TRBP cuts off the loop part of the stem loop to make a double stranded RNA duplex.  One strand (21-23 nt) becomes the mature miRNA and is loaded into an Argonaute protein while the other strand is degraded.  

siRNAs are made from longer double stranded RNA precursors.  Double stranded RNA is cut by Dicer into small (~21 nt) double stranded RNA duplexes.  These are also loaded into Argonaute proteins.  These long double stranded RNAs can be due to viral infections, mRNA-pseudogene RNA duplexes, or overlapping transcription of opposite DNA strands.

Small RNA duplexes that are artificially introduced into cells are also called siRNAs but they end up in the same effector complex as miRNAs.
   
Once these small RNAs are loaded into an Argonaute, they act exactly the same.