All of the nonuniform generators use the same uniform generator as the basis for their algorithms.
The Inverse Transformation method is based on the property that the cumulative distribution function for any probability distribution increases monotonically from zero to one. Thus, the inverse of this function can be computed using a random uniform variate in the range (0, 1) as input. The resulting values then have the desired distribution.
The Direct Simulation method actually performs a series of experiments on the selected distribution. For example, if a binomial variate is being generated with Prob = .5 and Trials = 20, then 20 uniform variates in the range (0, 1) are generated and compared with Prob. The number of uniform variates found to be less than Prob then becomes the value of the binomial variate.