These two measures of time will only be the same if all of the assumptions which go into the conventional radiocarbon dating technique are valid.Comparison of ancient, historically dated artifacts (from Egypt, for example) with their radiocarbon dates has revealed that radiocarbon years and calendar years are not the same even for the last 5,000 calendar years.Other radiometric dating methods such as potassium-argon or rubidium-strontium are used for such purposes by those who believe that the earth is billions of years old.
Some organic materials do give radiocarbon ages in excess of 50,000 "radiocarbon years." However, it is important to distinguish between "radiocarbon years" and calendar years.
The slope of the line determines the date, and the closeness of fit is a measure of the statistical reliability of the resulting date.
Technical details on how these dates are calculated are given in Radiometric dating. As with any experimental procedure in any field of science, these measurements are subject to certain "glitches" and "anomalies," as noted in the literature.
Here is one example of an isochron, based on measurements of basaltic meteorites (in this case the resulting date is 4.4 billion years) [Basaltic1981, pg. Skeptics of old-earth geology make great hay of these examples.
For example, creationist writer Henry Morris [Morris2000, pg.