The decay time of a source, as you have probably seen, is not exactly predictable; rather, it can happen at any time but tends to occur near a certain 'mean' time. In other words, just like a plinko game, there is a distribution of values which theoretically extends from t=0 (short decay time) to t-->infinity (long decay time). It looks sort of like a bell curve, and it is called either a Gaussian or Poisson distribution, depending on the number of events. Since these functions technically have infinite width, a convenient reference to use is the full-width-half-maximum or FWHM value. See http://www.physics.sfsu.edu/~bland/courses/490/labs/b2/b2.html for details.
If you look at your Gaussian on a plot of # of decays vs. decay time, you see there is a certain time where the number of decays peaks. This maximum is sometimes called the mean decay lifetime. The "distance" (in this case time) between the half-maximum values, which occur on either side of the peak, is the FWHM. The narrower the FWHM, the more likely a source will decay within a certain range of its mean value. See Wikipedia "FWHM" or the web page mentioned above for a decent picture of this.
So sources that have narrow FWHMs have very predictable decay lifetimes, which can be useful. I believe one of the drawbacks of carbon-14 dating is that, the older the organic sample is, the wider the FWHM value is and therefore the harder it is to date with good statistical confidence.
I don't know why two different Th-230 sources would have different FWHM values; this could either be normal statistical variance or it could have something to do with the purity or age of the sample. I would think that the older a sample is, the less predictably it will decay, since much of the sample has already decayed into something stable and you have just a few unstable nuclei left. However, I think the mean decay lifetime should be the same no matter what the age of the sample is. Was this the case?
