Does A digital signal consists of a continuous electrical wave?

Digital signals are virtually always transmitted using a continuous (analog) waveform. Even a signal that is called "digital" is actually analog in practice.

When a digital signal is transmitted over short range (inside an integrated circuit, on a computer motherboard, etc.) we talk about it being digital, but inspection of the actual waveform with an oscilloscope will reveal that it is not just two different voltage levels. But it is "mostly digital" and can be treated as such by circuit elements that are expecting digital signals. That is, we call it a "digital signal" but it isn't perfectly digital (two different values).

It is actually theoretically impossible to transmit a pure digital signal. Doing so would require an infinite energy pulse to create the step functions. In practice, the limiter to making a signal that is almost perfectly digital tends to be the "load" and the transmission channel, which both have resistance, capacitance and inductance that make even a very abrupt signal smooth out a little.

When digital signals are transmitted over relatively long distances, they are sometimes deliberately "encoded" onto an analog carrier. There are various methods for doing this, such as frequency modulation, amplitude modulation, phase modulation, or combinations. There can even be multiple layers of encoding to implement features such as error detection and error correction. So if you were to inspect the signal that is transmitted, you would see an obvious analog signal, but the information that is hidden in it is an encoded digital signal that will be re-formed at the receiver.