is a specific kind of: approve, O.K., okay, sanction.

is a broader term that covers: guarantee, warrant | champion, defend.

verb group: back, endorse, indorse, second.

derivation: support | backing, backup, championship, patronage | endorsement, indorsement | blurb, endorsement, indorsement | endorser, indorser, ratifier, subscriber | admirer, booster, champion, friend, protagonist, supporter | supportive.