It's known not to be the same. In particular, the matter created in the lab is far too hot.

Particles can't be "too hot": that's an English description, not a scientific description. And as the article does not talk about energy levels (the word "energy" is used exactly once), or eV values, or anything relating to your claim: where'd you get that idea?

A lot of particle accelerators don't accelerate elementary particles. They accelerate nuclei, which can turn into a blob with a well-defined temperature when they hit head-on.

Yep, but that still leaves out the critical part where we're not talking about in general, we're talking about this study, which is about neutron stars, made famous by the fact that are not composed of nucleic matter.

Your objection is without merit. Neutron stars also have temperatures.

So does coffee, what are you guys talking about?

I'm pretty sure they're saying the same thing, but just being very pedantic and/or using layman terms versus non-layman terms. Temperature versus energy?

Honestly, I got lost part of the way through.

I pointed out heavy ion collisions are not appropriate for studying neutron star matter (because the temperature is far too high). He objected for a spurious reason, I pointed out he was wrong, and he came back with something irrelevant. I can't explain why he's doing that, but his comments are what they are.

To my knowledge, what's happening here is that there is a single phenomenological input, the equation of state, which is relevant in both neutron stars and heavy ion collisions. Different theories will predict different equations of state, but you can experimentally constrain it either through astrophysical observations of neutron stars, or through smashing gold atoms.

It isn't just a guess that these things have some similarity, our theories very confidentally tell us that both situations are best described as QCD matter. The properties of this QCD matter, including the equation of state, is the fundamental science question that is of interest here.