Definitely agree on differentiating between rewards / recognition!
On recognition, one of our offices has a monthly all-staff meeting with 5 minutes of values shout-outs at the beginning. At each meeting they choose one value and send an email in advance defining the behaviors associated with the value and asking staff to write a shout-out related to that value for one person on a sticky or index card. Then we do a popcorn/lightning round where people read theirs, and at the end everyone gives the card to the staff they shouted out (even if they didn’t get a chance to say publicly).
We also have annual values (we call them cultural tenets) awards where people vote on who exemplifies each tenet – that comes with a small cash prize.
And yes, regardless of recognition I think it is super important that your values have well-defined behaviors associated with them (and sometimes which behaviors are NOT those values) to make them meaningful.