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When you decline rewards, nobody will get any reward.
When you select burn, the author's payout is burned but the curators still get their reward.

When you decline the rewards, all the rewards go back to the reward pool, including the curation rewards. (this is different than setting beneficiary)
If you want to keep the curation rewards, you can set the beneficiary to @null to burn only the author rewards. Although I would recommend setting beneficiary to @hive.fund or @hbdstabilizer for sending the author rewards to the DAO instead of burning them.

Thanks for clarifying the difference @arcange and @mahdiyari. I previously thought burn was all going to null and decline rewards was author and curation rewards going back to the pool (both of it). Burn seemed like a better choice because I still want curators to get their curation returns but I forgot Hbdstabilizer was also active so that makes it even a better program to support to.