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The first indicates the proportion of radiocarbon atoms in the sample as compared to samples modern in 1950.
The second is directly derived from this on the assumption that the half-life of radiocarbon is 5568 years and the amount of radiocarbon in the atmosphere has been constant.
This method will tell you the years in which the radiocarbon concentration of tree rings is within two standard deviations of your measurement (e.g.
Since the calendar age of the tree rings is known, this then tells you the age of your sample.
In practice this is complicated by two factors: These effects are most clearly seen by looking at a specific example.
The pair of blue curves show the radiocarbon measurements on the tree rings (plus and minus one standard deviation) and the red curve on the left indicates the radiocarbon concentration in the sample.
The grey histogram shows possible ages for the sample (the higher the histogram the more likely that age is).