davee123 at BrickSet describes it this way (using LEGO Part Number for element ID):
A "Plate 2 x 3" has a LEGO Design ID of "3021". But for a "Dark Green Plate 2 x 3", you have a LEGO Part Number of "4297717". And for a "Sand Blue Plate 2 x 3", you have a LEGO Part Number of "4153276". So different LEGO Part Numbers for each combination, but with the same LEGO Design ID for each.
Peeron, BrickLink, and LDraw use the *combination* of the LEGO Design ID and the color ID in order to reference a particular instance of a part. But LEGO uses the LEGO Part Number. They do that because effectively, in a production line, they want a robot to go pick up parts from "bin X". The robot shouldn't care what the LEGO Design ID is, or what the LEGO Color ID is, so they use that separate numbering system.
For a lot of parts, hobbyists don't know what the LEGO Design ID is-- like for a Super Battle Droid arm. When it got entered into the Peeron system, since they didn't know the LEGO Design ID, they had to invent a new number, so they arbitrarily used "x387". Similarly, when BrickLink entered it into their system, they ALSO didn't know the appropriate number, but they also didn't co-ordinate with Peeron (or visa versa), and so they wound up with "x280". In that case, we actually know that the LEGO Part Number for Battle Droid Arms in Pearl-Dark-Gray is "4499247". But as a community, we still don't know what the LEGO Design ID is for that element (or, at least, I don't think we do!).bsf
Finding the Element ID
Distinguishing Types of Numbers
If you are unsure about whether a number is a LEGO element ID or a part number, a good way to tell is the number of digits. LEGO element ID's have 6 or 7 digits, while part numbers typically have 4 or 5 digits. Also part numbers can often be found molded on the physical piece itself in a tiny font (smaller than the word "LEGO" on a stud.)
Using Instruction Booklets
LEGO instruction booklets which list the set inventory usually list the LEGO element ID next to the image of the element.
- Find the element you want, possibly by browsing “Catalog” then “Parts.” One need to end up on BrickLink's Catalog Entry for the element. You can get here in a variety of ways. One way is to click on the image of a part you want, which will show a larger image. The larger picture will always have a link to the Catalog Entry page.
- At the entry page, look at the links below where the picture is. One of these links should read “View Small Images.” Click on it. This will bring up all the pictures of the piece in all its colors.
- Below the pictures is a table titled "Part Color Codes:". The second column, under the heading "Code", contains the element ID. Copying then pasting this number in a BrickLink search, will pull up that particular piece in that exact color.
Note: sometimes the same color is listed multiple times. This indicates that the color was issued, discontinued, and reissued a number of times. To the right of the element ID should be another number. This will tell you which entry came out before others. For example, you can have three entries. They will have a 1, 2, and 3 to the right of their ID. This means the one labeled “1” is the oldest and “3” is the newest since it was issued last. In cases like these, it is best to only take the element ID that is the newest when using it to deal with LEGO. Otherwise, their system will just tell you that the piece is discontinued.tb
Finding Pictures of Elements
You can enter the element ID in the BrickLink search box and for most elements it will take you to the page for that part and tell you what color the ID number codes for. This depends on BrickLink contributors adding that element ID to the BrickLink catalog, so new parts might not be in there yet. Once you're on the BrickLink page for the part, you can get small images in different colors.