If you look for amplitude, frequency, phase modulation, you typically get some picture saying you have a wave and you modulate the corresponding parameter (amplitude, frequency, phase). On the other side, if you look at how digital communication is happening, people say that you have a series of delta impulses (or rectangular signals) representing the data, put that into some transmit-filter that is doing pulse shaping, multiple that by a carrier frequency and emit the signal by the antenna (they call it "sending pulses"). Before it is shifted to the carrier frequency, you have that sinc-function signals that somehow overlay with each other.
I can imagine that in an analogous amplitude modulation case it is enough to multiple the low-frequency baseband signal with a carrier frequency, and get it back on the other side with a similar technique. However, if we go now to a digital signal, can I then do the same with delta impulses that are fed into a square root raised cosine filter that is then multiplied with the carrier frequency? Is that amplitude modulation? However, I have no idea what that should look like for phase shift keying or even frequency. How does a transmit filter chain look, if I have digital signals? It is confusing that some people talk about sending pulses and others about sending waves.