I'm currently learning how to play a few songs. Two are from sheet music, and one is from watching a guy play and copying him.
Without trying, I've memorized the copied song, but not the sheet music songs.
The songs also *feel* different inside me -
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like, the copied song feels very synesthesia-heavy; it feels like it has physical mass and clear orientation, whereas the sheet music songs are much more 2d; they feel as though they exist inside me only as fragmented parts.
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Are you familiar with Iain Mcgilchrist's book, The Master And His Emissary? It's all about these sorts of differences in experience, and, well, consciousness.
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When I learned piano as a child, each week I’d have a “book song” (sheet music) and a “by ear song” (copying someone). I can sort of fumble through sight-reading, but when I hear a song now, I can 100% feel the notes and chords in the way you describe (and then I can play it!).
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This means that you‘re a visual learner. It’s quite common. The sheet music song will come to you, eventually. The reason that it will take longer is because you will have to come up with your own technique and flow that was already given to you in the copied song.