A digital signal can be discrete or continuous. A digital signal can only have a set of finite values. If the digital signal is *binary*, it can only have 2 values, 0 or 1. A PWM signal is an example of a continuous signal (NOT discrete), and binary digital having just 2 values. A discrete signal is one that is defined only at specific time intervals. If an continuous analog or digital signal is sampled at some rate, the sample set is a discrete signal. If the sample rate is 1.0 kHz, then there is a sample value every 1.0 milliseconds. This can be digital or analog. If the signal is analog (continuous), it can have any value, i.e. the vertical axis value is not restricted. But the horizontal time axis has values defined only at the 1.0 msec sample points.
Summary: a digital signal can only have discrete values, for binary digital those values are 0 and 1. A digital signal can be continuous in time, such as a PWM signal. Or it can be discrete, where the data exists at specific values of time. An analog signal sampled by an A/D sample and hold is converted to a discrete analog signal. Then the A/D converts it to binary digital, i.e. 0 and 1 values only.
I hope I helped. A great text is the signals and systems book by B.P. Lathi.
Claude