The second is analyzing the law, and finding a provision that conflicts with a provision of the constitution. It’s not very formal, but it’s more than opinion.
It’s not quite that pure. If there are self-contradictions in the constitution, then that gives them some choice about what to compare the law to. They ought to balance that appropriately, but their biases surely creep in.
The Supreme Court issues opinions. That's the actual word they use to describe what they write. You can either form an opinion or you can discover a truth. The Supreme Court does not discover whether it is true or not that a law is constitutional or unconstitutional. Each member forms an opinion, and whichever consensus opinion includes the majority of justices, that becomes the opinion by which other courts proceed to interpret the law.
You might want to mask "discover the truth" with "finding a provision", but the Supreme Court does not "find provisions that conflict with other provisions", they interpret things to form opinions. In this case 5 of them interpreted a provision to be in conflict with the way they interpreted a provision of the constitution. 4 of them did not share either or both of those interpretations.
It’s not quite that pure. If there are self-contradictions in the constitution, then that gives them some choice about what to compare the law to. They ought to balance that appropriately, but their biases surely creep in.