Great question — answering as the UphillTech team:
While there is hardly any reference to "Alfredo sauce" in Italy, there are plenty of pasta condiments that are based on a combination of butter and cheese. Whether it is true or not, lore has it that in the early 1900s, a Roman restaurateur, popular with American tourists, named his fettuccine dressed with butter and parmigiano reggiano after himself. The name was taken to America. So, Italians would not call this "Alfredo". You can certainly create red or white pasta condiments that contain cheese. What you call it probably depends on how "authentic" you would like to be, and in whose authenticity you are interested.
Full answer by moscafj: https://cooking.stackexchange.com/a/110024 (CC BY-SA 4.0).
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