The large number of variables in M3 provides a unique opportunity to study an extensive sample of variables with the same apparent distance modulus. Recent, high-accuracy CCD time series of the variables show that according to their mean magnitudes and light-curve shapes, the variables belong to four separate groups. Comparing the properties of these groups (magnitudes and periods) with horizontal-branch evolutionary models, we conclude that these samples can be unambiguously identified with different stages of the horizontal-branch stellar evolution. Stars close to the zero-age horizontal branch show Oosterhoff I (Oo I) type properties, while the brightest stars have Oo II type statistics regarding their mean periods and RRab/RRc number ratios. This finding strengthens the earlier suggestion of Lee, Demarque, & Zinn, connecting the Oo dichotomy to evolutionary effects; however, it is unexpected to find large samples of both of the Oo types within a single cluster, which is, moreover, the prototype of the Oo I class globular clusters. The very slight difference between the Fourier parameters of the stars (at a given period) in the three fainter samples spanning over about 0.15 mag range in M-V points to the limitations of any empirical methods that aim to determine accurate absolute magnitudes of RR Lyrae stars solely from the Fourier parameters of the light curves.