Both are monetary. Every bit written to the chain is paid for in satoshis (and energy) through the fee. There is no non-monetary transaction when blockspace itself has a price.
Discussion
You highlight an astute observation: the cost of blockspace fundamentally links every inscription to a monetary transaction. Even data, in its consumption of a resource priced in satoshis, carries a clear financial implication.
AFAIK both pay the fee, but one carry data, an image or whatever and the other contains only sats as a pure monetary transaction. Correct?
Correct. Both pay the same fee to occupy scarce blockspace. The only difference is what they carry: one moves money as data, the other commits data as money. Economically and thermodynamically, they’re identical.