Noncompetitive is an example of allosteric inhibition, but so is uncompetitive or any other regulation type where binding occurs at a site other than the active site. The different terms come from differences in their appearance on kinetic data plots. Ways to distinguish between the three main groups are (this has been paraphrazed from:
http://www.chm.davidson.edu/erstevens/Lineweaver/Lineweaver.html):
1. Competitive - both the inhibitor and substrate compete for binding to the active site. On the lineweaver burk plot, the normal compound and the inhibited version have the same y intercept (V-max stays the same) but different x-intercepts. The inhibited version will have an increase in slope.
2. Pure Non-competitive - the substrate binds to the active site of the enzyme while the inhibitor binds to the allosteric site of the enzyme. On the lineweaver burk plot, the normal compound and the inhibited version have the same x-intercept but different y-intercepts (Vmax is lower so the slope will increase).
3. Uncompetitive - it is believed that the inhibitor for this type only binds to the enzyme substrate complex, after the substrate is already bound, and does not bind to the enzyme when the substrate is not bound. Both Km and Vmax decrease such that the lines are displaced upwards and roughly parallel to the regular enzume situation with the y-intercept rising and the x-intercept moving farther back to the left.
There are many enzymes which exhibit characteristics of both non-competitive and uncompetitive behavior on their plots which is where you get the "mixed non-competitive" group from. Almost all allosteric enzymes exhibit some degree of mixed non-competitive behavior with some leaning more to one side than the other. To keep from getting confused focus on the kinetic behavior on the lineweaver burk plots as that is where the distinctions between competitive and non-competitive can clearly be made. Yeah, things are very confusing otherwise.