What is the distinction between the first and second of the Ten Commandments? For many years the two subconsciously blurred together in my mind. My assumption was that when you make an idol you are worshipping a false god, and so I basically just heard both commandments to be saying, “Don’t do that.”

Puritan authors saw a clear distinction, though, between “no other gods” and “no graven image.” They consistently taught that the first emphasizes WHO is to be worshipped while the second emphasizes HOW He is to be worshipped. One regulates the object of worship and the other the manner of it. We could put it this way:
#1 Do not worship false gods.
#2 Do worship God falsely.

One of the strongest cases to be made for parsing the two commandments in this manner is based on the very thing that was happening at the foot of Sinai while these commands were being given! If you haven’t already, be sure to take notice of whom the golden calf was dedicated to:

“And Aaron made a proclamation and said, Tomorrow shall be a feast to YHWH’”
(Ex 32:5).

Many English translations will say “the LORD” there, but such capitalization indicates that the underlying Hebrew text uses the Tetragrammaton, the specific holy name of the covenant God of Israel. The golden calf wasn’t made for Baal worship, it was made (ostensibly) for worshipping that very same Jehovah who brought the Hebrews out of Egypt! They weren’t worshipping false gods, they were worshipping the true God falsely.

Indeed, the golden calf incident is likely at least part of the background behind Matthew 7:21. Saying, “Lord, Lord,” to Jesus while not doing the will of His Father is the same as bowing down to a golden calf while declaring praises to Yahweh. Merely vocalizing the correct name of God does not acceptable worship make.

And again, the golden calf is the primary intertextual reference which the “image of a beast” in Rev 13:14-15 intends to evoke in the neural pathways of the Biblically literate reader. Don’t conflate the beast of the sea (the first half of Rev 13) with the beast of the earth (the second half); they are different threats. The former is the one you’ve probably been warned of the most, the one who uses fear and coercion to push you to explicitly deny faith in Jesus. And, yes, that is indeed something to be on guard against, especially in certain times and places. But the latter beast is much more deceitful and subtle. The modus operandi of the false prophet is imitation and forgery. He’s not out to cover over the soil of your faith with rocks, but rather to fill it up with thorns. He sees that “Yahweh”, “Jesus”, “Christianity”, and “the Bible” have a highly successful brand name going and, instead of swimming against that current, infiltrates the movement to promote his own franchise chain of knock-off products based on the originals. The mark of the beast isn’t so much about “worshipping Satan” (not explicitly, that is) as it is about presuming to “worship” the true God but doing so in a Satan-inspired manner.