The conventional definiton of a Digital signal is as follows: A digital signal is a signal that is discrete in time and quantized in amplitude. Almost all resources (textbooks, online sources,etc) stick to this defintion and gives emphasis to the point that a digital signal is discrete in time.
A binary signal is a Digital signal.
But according to the defintion, the signal should be discrete in time to be a digital signal. In the plot, a binary signal is drawn as continuous in time. Then how can this be a digital signal according to the defintion.
Also I read that a digital signal has different meaning/definition in different contexts. For example the above mention definition is apt in the signal processing context, whereas in digital electronics where the binary signal mention above is used, a digital signal is a signal that takes only discrete amplitude values(ie. it is quantized in amplitude) and it can be continuous or discrete in time.
I am confused that why is the above definiton given a strict emphasis even in digital electronics context usually. Almost everywhere I look in internet and even some teachers give the conventional definition of a digital signal without mentioning the context.
Are my above findings correct? I would like to know the exact definitions of a digital signal according to different contexts.