I saw there are different types of derivation path in ledger live. One is 44'/1729'/0'/0'. Another one is 44'/1729'/1'/0'. What does the third slot mean? What does each slot mean? Ledger live seems to only have one type of account, so I wonder when ledger live uses the third slot. They don’t seem to have a rule to pick between third slot and fourth slot.
The third slot (level) of the derivation path is an incrementation index. For more details, see bip-0044. More specifically, the third level discriminates different accounts. This allow a wallet to generate discriminate keys for different purposes (consider e.g. a checking account, a savings account, ...). You can read more here.