I think you want them to be meaningfully different, for whatever reason, but at the end of the day, they both come down to "if I did the thing you already did, and that you laid claim to through some form of artificial statutory fabrication of rights, you can sue me".
Whether that means me exploiting having heard your song by playing your song myself, or exploiting your invention I examined by building it myself, they both come down to: statutory fabrication of fictitious "you can't do because they did already" rights, that at common law could have (rightly) only been achieved through keeping the thing a secret (e.g. still present to this day in say trading algorithms, and in software through the now ubiquitous SaaS model) and contacts (i.e. NDAs) flowing from that.
See my other reply parallel to yours. There's no principle of "I did it first, therefore it's my property!". For example, if that was so, you could report an invention and get a patent for it without disclosing exactly how you did the thing. After all you did do it first, so it should be off limits by the (non-existent) "I did it first" principle. Instead, patent law requires "sufficiency of disclosure", meaning that you MUST disclose enough information that another skilled person can recreate the invention from the specified information. You get the time-limited exclusivity in exchange for disclosing the method so that others can work on top of it, refine the technique etc, so when the time comes that the patent expires, there will be improved versions. It is explicitly there to inspire others to work on the thing afterwards, just with some time delay.
Blurring distinct laws and their nuanced purposes into some generic "I call dibs!" principle is exactly what the propaganda part is. Because that creates a kind blurry haze in people's minds that even fills gaps that none of the existing laws currently block out. So people will feel like "that just feels illegal, but I can't exactly say what it violates". A kind of FUD around doing all manners of free intellectual activity in society.
Whether that means me exploiting having heard your song by playing your song myself, or exploiting your invention I examined by building it myself, they both come down to: statutory fabrication of fictitious "you can't do because they did already" rights, that at common law could have (rightly) only been achieved through keeping the thing a secret (e.g. still present to this day in say trading algorithms, and in software through the now ubiquitous SaaS model) and contacts (i.e. NDAs) flowing from that.