What are the names and categories of LEGO bricks? Is there a consistent naming scheme? Does Lego have an official name or identification for different pieces?
It's been worked out by multiple groups who decided on different systems. The disagreement is based on what information was publicly available from the Lego Group at the time, what pieces had been manufactured up to that point, and what features the category authors thought were salient.
To really appreciate the magnitude of the problem, just try classifying every part in your own collection. Make your own categories or try to follow somebody's elses. You will raise a lot of questions about how broad the categories should be. Everybody with a storage system goes through this.
Existing Classification Schemes
In the end, some parts are placed into categories primarily by geometry, others by function, yet others by historical origin. You could also conceivably group bricks by building function (I'm thinking of direction-changing rectilinear bricks) or even by simply the number of studs (I'm thinking of a Kanji dictionary.)
Part Names Make Classification Muddier
Consider the language barrier: if you read Lego's English Pick-A-Brick names, you realize it's translated (from Danish). A major category is "Brick, Bow" also known as an Arch.
Consider 30367, LEGO's "Final Brick" filed under Bricks, Special. Perhaps they meant Finial? LDRAW calls it a Cylinder with Dome Top. BrickLink puts it under Brick, Round (remember BrickLink has both categories Cylinder and Brick, Round from its LDRAW heritage.)
Jumper Plate is one name that made perfect sense to Europeans but baffled Americans; to James Jessiman (Australian) it was a Plate 1 x 2 with 1 Stud. I recall Auczilla used the adjective Offset in there. In Pick-A-Brick it's now a Plate 1x2 With 1 Knob. Or should it be a tile because it's mostly flat?
Then there are multi-purpose parts: describe 4349 geometrically and it's another cone. But it could be a Minifig Weapon, or just Minifig Utensil. In LDRAW, it's a Loudhailer and has no category as such. The American term would be a Megaphone but many know it as Star Wars Blaster.
Multiply this complexity by thousands, and you get an idea that the task of naming is never settled.
Many LEGO bricks have part numbers imprinted from the mold. This is now called a "Design ID" by LEGO. It served as the original basis for LDRAW part numbers. However, LDRAW invented its own numbers for parts with no number.
About the year 2000, LEGO introduced a 7 digit "Element ID" to designate a particular design in a particular color. These numbers began to be used internally at LEGO for Building Instructions software, and externally in LEGO Creator software products. They are now shown in official set inventories and in Pick-A-Brick.
This should give you an idea why different name and category schemes don't align. We start by talking about the same LEGO pieces but we bring preferred names from childhood or later (I always referred and still refer to 1xN bricks as 1-bumper, 2-bumper, etc.) We group them according to geometry or function, but find new reasons to subdivide or revise to make the groups more intuitive. New parts challenge these categories. LEGO does not seem to have given the problem much thought or care, lumping parts into catch-all categories. I derive immense satisfaction from solving a problem of devising a part's genus and differentia, but I realize that just like in the taxonomy of living things, there is competition between systems, and endless revision.