Waived - A non-vested player (less than four years of service) who is terminated goes through waivers. When he is released another team can claim him within a certain period of time. A vested veteran only goes through the waiver system from the trading deadline in midseason through the end of the season. During the offseason and all the way up to the trading deadline, a vested veteran gets released.
Released - A vested veteran is free when he is terminated and can sign with any club. Keep in mind, if the termination takes place between the end of the trading deadline and the end of the calendar year, the player goes through waivers. A vested veteran released this time of year is free to sign with any team.