> In my mind, “user” stated to take over when we started having web based services that were used by people

Maybe I'm just old, but we've called ... users ... 'user' since Unix or before. Perhaps it is just because Unix was integral to my early computing experience that I see it that way.

User is definitely a term that long predates the modern SaaS world. And it’s an appropriate term in many cases because even today the customers of a computer hardware or software company are often not the same people using that hardware or software. I am the user of my work computer, but even as a software developer I am certainly not the “customer” of that purchase. My company has requirements as a customer that might be counter to my desires as a user. And likewise I have needs as a user that my company as a customer does not care about (except in so far as having those needs met allows me to do my job)