E.g. "Negative Energy Plane", "Elemental Plane of Air", "Material Plane", essentially all the inner planes plus the material plane: Are these considered Product Identity or could I use them for other projects, commercially or otherwise?
So to go into this in a little more detail...
Copyright, trademark, and other IP law is a whole separate standalone thing. If they have a trademark on those terms they'd be registered. I suspect those terms are general enough there's no trademark per se. In fact, you can find out. Check out this TESS search for "dungeon" which reveals "Dungeons & Dragons," "Dungeon Dice," and a lot of the predictable things. But searching on "elemental plane" etc. shows nothing. As for copyright - you can copyright fictional characters and settings and other constructs but only under a specific set of restrictions given precedent from the US courts. Hasbro could probably say that the standard D&D Multiverse is a distinct enough setting that it's copyrighted. Just a "prime plane" or an "elemental plane," not so much. In a related note, you cannot copyright game rules, though you can patent them (like trademarks, patents are registered so if there's not one then it's not patented).
The OGL is something you sign up for if you want to use those tasty d20 rules (or several other rule sets that also use the OGL license). If you use that, then you are not allowed to use anything designated as Product Identity, which is something defined exclusively by the contract which is the OGL, and includes those and every other proper noun in the book(s).
Those are two completely separate things. As an illustration, Mayfair made a bunch of Advanced Dungeons & Dragons (1e) compatible supplements back in the day. They got sued and had to stop. Why, because of IP law? Nope. Because they had signed some agreement with WotC at some point that said they couldn't do that.
Note all the people publishing "5e" supplements without a license right now, Kenzer & Co. and others did it with 3.5 and 4e as well. Hasbro lost a big lawsuit along those lines to RADGames, some guys who made a Monopoly add-on. "Here's a cool set that fits inside the board! Good with Monopoly (tm)!" Judge says - a) you can't copyright game rules and b) that's completely legal, STFU Hasbro. With the caveat that someone always can sue you, they don't have to have any sort of good legal reason to do it, getting around IP law for publishing compatible products is doable. However, if you have engaged in any agreement - and the OGL is an agreement - it can constrain you from doing lots of things.
So in general "if you don't know the difference between these terms you should probably stop thinking about doing whatever you're doing," but it is feasible.
The OGL is not about copyright. It's main purpose is to create an artificial trademark by getting authors to include (and implicitly agree to) a license which defines certain things to be "Product Identity". Many of these things are indeed already trademarks (the system name, for example) but some, such as "Mind Flayers" are not.
The upside for the author is that it makes it harder for Hasbro to sue them for producing material, something that TSR tried in the dark days of 2e (and sometimes even in the happy days of 1e). The downside, of course, is that you can't use terms like "Mind Flayer" in your work, as you legally could without the OGL. In a similar way, no special permission was ever needed to quote small sections of rules for discussion (e.g, spell descriptions) but the OGL grants/restricts rights to use certain abbreviated versions of the rules in a bulk fashion dictated by Hasbro.
The relationship to copyright is said by some to be that the OGL rests on copyright. This is is only superficially true. While it is the case that without copyright anyone could print any amount of material quoted from the rules or other works, the fact is that the OGL is not concerned with people trying to make their own reprints - that is already done by copyright law. What the OGL specifically brings to the table are restrictions on new material such as scenarios and settings, something which copyright is totally unconcerned with because, obviously, no copying is involved.