Time Delay Control (TDC) for linear and nonlinear systems with uncertain dynamics has been widely discussed in the literature, as it has a very simple and compact form. It uses time-delayed signals for estimating unknown dynamics at an instant, and uses feedback linearization for cancellation of known and estimated unknown dynamics. While the original formulation and most of the analyses have been focused on the continuous version of the controller, its implementation is more natural in digital form. This paper extends the recently improved sufficient Bounded Input - Bounded Output (BIBO) stability conditions for continuous Time Delay Control of nonaffine nonlinear systems to discrete Time Delay Control, including simplified approximate conditions under various assumptions. Additionally. asymptotic stability is established for similar conditions. The derived conditions are contrasted with earlier results for continuous Time Delay Control. Examples are used to illustrate the differences in continuous and discrete TDC, related to performance as well as sufficient and actual conditions for stability.