They both mean the same noun, yet one is spelt with a capital?
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Unless there are specific rules in place, such as for particular documents or particular prescribed styles, "state" follows the same rules as any other word, capitalised when it's a proper noun or part of a proper name.
If you look at the Wikipedia article titled United Nations General Assembly Resolution you'll see that it lists:
Resolution 273: Admits the State of Israel to membership in the United Nations.
"State of Israel" being a proper name, so capitalised by Wikipedia.
Resolution 62/149: ... Calls on states which have abolished the death penalty not to reintroduce it.
UN GA Resolution
The Wikipedia article has not capitalised "states" because it's not a proper noun here.
Resolution 67/19: Recognizing the State of Palestine as a non-member observer state.
Wikipedia has capitalised "state" in "State of Palestine" because it's a proper name, but not observer "state".
However if you look in the UN resolution:
...to resolve the status of Jerusalem as the capital of two States.
UN GA Resolution_67/19
Here you'll see that "States" is not part of a name, yet capitalised anyway.
Noting that, in the judgment of the Security Council, Israel is a peace-loving State and is able and willing to carry out the obligations contained in the Charter,
GA Resolution 273
The UN Resolution document has capitalised "state" even if it's not a proper noun, because this is their style on official documents.
The same discrepancy is seen all over the place with all sorts of words. Governments, councils or any organisation will have their own rules and style.
Another common example is "act" as in legislative act.
- (Law) (capital when part of a name) the formally codified result of deliberation by a legislative body;
Collins English Dictionary
Here Collins Dictionary is telling us to capitalise "act" when it's part of a name. You'll see some variation in this word's capitalisation when not part of a name.
I've seen it capitalised in Wikipedia and BrE news media articles.
So basically whether certain words are capitalised when not proper names depends entirely on what rules are being followed by a particular government, organisation etc.