They're inherently different: creative work (especially in a digital, trivially replicated format) is non-rivalrous, and at least partially non-excludable. "You wouldn't download a car." [0]
Property rights are a social technology to balance incentives and peacefully negotiate scarce resources (including time and effort). It's helpful to think about them in reverse: that they encode legitimacy to use force (usually via the State) against anyone who violates the right. That doesn't make the force right or wrong, a priori; it simply describes what happens. Exactly when that force is legitimate is the question at hand.
"Intellectual Property" is a post-hoc neologism. What we actually have are three very specific institutions: copyrights, patents, and trademarks. The last is arguably more like regulation than property: persistent brand identity to prevent fraud and confusion. Copyrights and patents are extremely clear in the Constitution, that their purpose is collective, moreso than an individual right for its own sake: "To promote the Progress of Science and useful Arts". Hence why they expire: at some point, the incentive has already been provided, and the body politic benefits more by their being open-sourced.
Whatever "rights" framework one subscribes to, it is an extremely thorny question, whether they include the right to alienate those rights, to give them up on purpose. We allow people to alienate their labor, an hour at a time; but not to do so for a lifetime (voluntarily sell one's self into slavery). Many US states now refuse to defend "non-compete" clauses: that you cannot constrain your future self from working for a competitor for X years, even if you wanted to, even for very lucrative terms in the contract.
I'd argue that intellectual/creative works, are more like non-compete clauses: you actually create more bargaining power if you limit the scope, and take away the capacity to give up future bargaining power.
[0] https://www.youtube.com/watch?v=V_gZZHu4TBk