The terms “binning,” “bucketing,” and “cutting” are all interchangeable jargon, used during feature engineering, to refer to certain quantization procedures. In particular, they are used to refer to a procedure that divides values into uniform intervals of either quantiles or values. These procedures are more formally known as quantile discretization (QD) and uniform quantization (UQ) respectively.
What these procedures have in common is that they divide something evenly. For QD, each “bin” has an (approximately) equal number of points; for UQ; each “bin” covers an equal range (except possibly the tails).