Crazymetalmonke did a decent job of explaining it. I forget exactly what the naming system is, honestly, usually though SG refers to the outermost part, which determine spin direction (and whether they are neo or normal SG 'shells'), I try to use "shells" as their name for clarity as I think the only official name for them was "SG's" which also refers to the entire assmebly. These do often get called casings, but I, and beywiki, generally reserve that for the next part, which is analogous to the core of Neo SG's (as well as the plastic inner part of a regular SG, which is considered a core itself), so, core and casings are generally used for that part, which is surrounded by the SG "Shells". The shaft is exactly what it describes, usually having the tip on it (Zeus' Shaft has a CEW attachment point instead of a tip, and Ariel 2's tip is considered analogous to a shaft). Bearings are the small metal rings, there are a few different kinds, but the only worthwhile ones are the shielded ball bearings (these appear and are significantly more complex than the cheaper single-piece bearings which are basically not worth using - only a shielded ball bearing lowers friction enough to make a real difference).
It's extremely easy to figure out if you actually have the parts, as it's all very much common sense, the new beywiki plastics combo formatting (hasn't been rolled out to all articles just yet but is on many) has the parts listed on separate lines, and going downwards they go from outermost to innermost, but you barely even need that.
Lastly, regular SG's also have a metal ring inside them, which has to be used with them (not using it causes looseness due to their design, unlike if the inner part from them is used in neo casings). IIRC this is called a "Metal Weight Gear" or something, I've actually posted the name before and don't have my books on me now, so I am probably wrong here.
Oh, and the bases and sg's are separate parts, though Metal Dragoon Bearing Stinger's base and SG part are officially considered one part, in future I will likely list them separately, even though the casings and bearings are the only part that is usable separately/exchangeable.
Of course, after that there's the matter of tips and what tips are/aren't considered part of the base and therefore not exchangeable, and those that are considered sg parts or something... Honestly the rule and the application of it make next to no sense, there's not much rhyme or reason to the parts takara did and didn't intend to be exchanged (though for what it's worth, all the information I can find indicates they were pretty lenient on a lot of things (though they were stricter on metal balls, only allowing the original amount, it's quite odd as 4 metal balls in Metal Ball base and SG Metal Ball Base seems to have been common even in japan, and is basically a staple customization for western bladers...)