There are three types of stereo B&O cartridges. The original SP series which fit the early decks with the round arm - BG1000, 1200, 3000 and Beocenter 3500 amongst others.
The next series was the MMC20 series which was around for some time which came in with the Beogram 4000 and was used in most readial decks with the square section arm - BG1100, 1500, 1602, 1900, 2200, 2400 as well as the 4002, 4004 and 8000. The range nomenclature is of the form MMC20X or MMCX000 except for two exceptions - the rare SP15 - which is an early form which became the MMC4000 and the MMC10E which was a US model.
The last models changed again and took a smaller cartridge - the MMC1, 2,3,4 and 5. Decks using this range included the BG1800, 2000, 3000 and the stacking decks - 5005, 5500, 6500 and 7000.
Soundsmith do have a list on their site but the confusion arises in that some decks share names! There are 4 different Beogram 3000s for instance. Feel free to ask if you need on here! We will always try to answer quickly! A type number of the deck is always helpful! For the 4002, I would recommend a MMC20CL if possible and nothing below a MMC20EN. The only problem with the Soundsmith range is that they are all black and don't match the arm. Excellent sound quality though.