>>11186507I see. I suppose you can think about them like that, but again, these are spherical harmonics - they only tell angular information, i.e. over a unit sphere. There's no radial information, which is where the s/p/d/f distinction arises, it's just angular momentum degeneracy.
And I'm not sure what the context of OP's questions are for, but I've always found the "probability of localizing an electron" thought a bit useless. True, sure, but who the hell is measuring electron-bound-to-nucleus positions? How does one even practically do that in the lab?
I think it's much more useful to think of orbitals in the second quantized sense, as just forming your Fock basis. These are the states that electrons occupy (to first-order approximation), Pauli exclusion forces occupation numbers to be 0 or 1, and each basis element has a certain energy that tells you in what order to fill them up. Hell, that's basically how high school chemistry teaches it, even if no one there realizes it.
