When people use the phrase in pop media, they usually mean something like "recommendation engine". Sure, it probably has some sort of novel algorithm involved, but you could just as well call it a "program". It doesn't sufficiently describe what you think you're describing.
It's a very broad and basic term, and now lay people are given the impression that the word means some sort of AI. They sometimes even half-jokingly talk about "The Algorithm" as some sort of mystical force.
I'm shocked that I'm basically the only computer person I know of who complains about this. No math people either! And at this point tech people seem to be misusing it.
I know this is a waste of energy and "algorithm" will go the way of "literally" but I don't want to go down without a fight.
Let "algorithm" go and accept that in most people's minds, knowing swap-sort makes you a sinister Illuminati manipulator, and using rot-13 makes you a criminal mastermind who trades small children for bitcoins on the darknet.