I think the concept of a "signal" depends on communication and includes the intend way of interpreting the message, otherwise there are just electrical waves or other physical quantities, which are not "signals" as such.
The defining feature of an analog signal is that the voltage of the source, for example, is analogous to some other quantity, like the pressure of a sound wave. Without such an analogy, there is not an analog signal in a proper sense.
Digital signals encode discrete symbols. When analog signals have a limited bandwidth and SNR, they can also be interpreted as discrete symbols by sampling.