What are the differences between micro RNAs (miRNA) and small non-coding RNAs (sRNA)? Are these two terms used interchangeably?
miRNA are one member of the small non-coding RNA family.
"Small non-coding" is a pretty broad term that encompasses microRNA and short interfering RNA, among other regulatory RNA species. The key word is 'regulatory'; each type of small non-coding RNA works by binding complementary sequences to exert some sort of regulatory control over gene expression. Someone more knowledgable might correct or add to this, but I believe that a key difference between the various types of regulatory RNA hinges on which other factors they recruit to their site of action.
Structural differences between these RNA are a little harder to characterize. This paper, for instance, discusses how miRNA have been found to play contradictory roles in gene regulation; repressing some genes, up-regulating others. The precise mechanisms behind this are an active topic of investigation, but a lot seems to depend, as I mentioned earlier, on which other proteins they recruit and this in turn, seems to be influenced by things like cell type and developmental stage, among others. Here's another paper , that goes into some of the sequence-based structural features of miRNA. I know that this one is free, but the first one might be behind a paywall. If it is, contact me & I can send you a pdf.
I don't hear the terms used interchangeably, however, at least not in the sense of someone saying "small non-coding RNA" when specifically talking about miRNA.
Small non-coding RNAs are NOT generally abbreviated as sRNA but as sncRNA, if anything. I say "if anything" because the "small" part is subjective and just a portmanteau descriptor. The straight answer to your question is as Forest has written: miRNAs are a specific type of small non-coding RNA, some of which appear to function in the regulation of gene expression — others remain to be characterized. Another problem with the 'small' epithet is that miRNAs may only be 20 nt in length, but are formed from pre-miRNAs of up to 1000 nt.
Other categories of small non-coding RNAs include:
tRNA (transfer RNA) - originally abbreviated sRNA (for soluble RNA) - involved in protein biosynthesis.
5S rRNA - a component of the ribosome
7SL RNA - a component of the signal recognition particle involved in recognizing the signal peptide of secreted and membrane proteins.
snoRNA (small nucleolar RNA) many of which act as guide RNAs in ribosomal RNA modification.
snRNA (small nuclear RNA) many of which are involved in the splicesome, the ribonucleoprotein complex which removes introns from precursor mRNA (these have names like U1, U6 etc.)
SINE RNA: RNA transcribed from the short interspersed nuclear repeats (SINEs - Alu sequences in humans) which are thought to be 7SL signal recognition particle pseudogenes.
And, no doubt, there are some I (and science) have missed.