A comparative study of different definitions of the beam width was made. It was shown that there were different values of the beam width in accordance with different definitions. The propagation of the second-order-moment-based width obeyed the ABCD law,and the propagation curve of the entropy-based width was approximately a hyperbola, but for the power-in the bucket-based width the ABCD law failed. There were nearly the same focal shifts of Cosh-Gaussian (ChG) beams for the second-order-moment-based width and entropy-based width, whereas it was not the case for the power-in the bucket-based width.