Isn't one just pictures & the other more arbitrary? It's all just recorded spam.
Discussion
Inscriptions "inscribe" data onto satoshis. Ordinals is an addressing scheme to reference the specific Satoshi. They work hand in hand.
* I am no expert. This is just what I've learned doing a quick investigation.
Pretty sure there is nothing ever actually tied to any satoshi. It doesn't move around with them as far as I know.