I was never clear on what decided whether or not a player could be sent or "optioned to the minors." Here are a couple definitions.
If a player is on the 40-man roster but not on the active major league roster, he is said to be on optional assignment—his organization may freely move him between the major league club and the minor league club. If a player is on the 40-man roster and not the active 25 man roster for any part of more than three seasons, he is out of options and may not be assigned to the minors without first clearing waivers. However, if a player has been optioned in three seasons but has less than 5 full years of professional experience, he may be optioned to the minors in a fourth season without being subject to waivers. A full season is defined as being on an active pro roster for at least 90 days in a season.
A player who is designated for assignment is immediately removed from the 40-man roster. This gives the team time to decide what to do with the player while freeing up a roster spot for another transaction, if needed. Once a player is designated for assignment, the team has ten days to do one of the following things: the player can be traded, the player can be released, or the player can be put on waivers and, provided he clears, outrighted to the minors. A player who is outrighted to the minors is removed from the 40-man roster but is still paid according to the terms of his guaranteed contract. A player can only be outrighted once in his career without his consent.