Even then, where does the Moon Lord come in in Terraria's official lore? I have a few pieces of evidence that may point to the Moon Lord and Cthulhu being one and the same, this evidence being taken from his Bestiary entry; which says the following:
"The mastermind behind all terrors which befall the world, freed from his lunar prison. Practically a god, his power knows no limits."
Let's take this entry step by step.
One, Cthulhu has multiple bosses connected to him, the most obvious ones being the Eye, the Brain, and Skeletron, as well as the three Mechanical Bosses. This pairs with the Moon Lord being "the mastermind behind all terrors which befall the world", which is most likely referring to Terraria's bosses. While Cthulhu is most likely not connected to all of the bosses in the base game, the description seems to fit pretty well nonetheless.
Second, both Cthulhu and the Moon Lord also seemed to be "locked inside a lunar prison" at one point. With Cthulhu being "sent to the dark side of the moon" by the dryads, it is good to assume the Moon Lord underwent the same fate before being freed.
As well as this, both the Moon Lord and Cthulhu could be referred to as gods, Cthulhu being an "unstoppable force" and the Moon Lord's "powers knowing no limits".
Along with all of this, the design of Cthulhu and the Moon Lord are relatively similar along with the Moon Lord's True Eyes of Cthulhu. Why would the Moon Lord's eyes have this name if the boss wasn't supposed to be Cthulhu himself?
Now, I'm not saying the Moon Lord being Cthulhu is fact, I simply gathered the evidence I could find to make a theory stating this. This said theory is plausible, and probably likely, but there's a chance it isn't correct. I would prefer if people would submit evidence supporting or undermining this theory in an effort to figure out whether it's true or not, or to create a better theory that is fact.