Here is my understanding:

In a poker tournament, a "re-buy" is a purchase of additional chips beyond the initial set of chips provided at the outset. Typically, re-buys are allowed within a set period of time or within certain levels when a player drops below a set number of chips, or even loses all of their chips.

An "add-on" is a purchase of additional chips beyond the initial set of chips and any re-buys without regard to the number of chips held by the player. In some tournaments involving a single re-buy, the "re-buy" is actually an "add-on" and may be purchased at any time, even at the start of the tournament. Add-ons are also typically allowed only within a set period of time or levels.

I hope this answers your questions.