A long time ago, both types of flags had the same type of behavior. Both would place the post into the respective community review queue and the private moderator flag queue:
- If review comes to a positive consensus or if the flag is manually reviewed by a moderator who decides the flag is correct, the flag is marked helpful.
- If community review disagrees with taking action on the post, and a moderator doesn't handle it from the moderator flag queue, the flag is marked disputed.
- If a moderator disagrees with the flag from their private moderator flag queue, the flag is marked declined.
You'll notice that it used to be the case that a "Leave Open" outcome on a recommend closure flag would also result in an outcome of "disputed", just like a "Looks OK" outcome on a Low Quality Posts task.
However, the system was later changed to never put recommend closure flags in the private moderator queue, as this effectively granted a privilege to lower-rep users that wasn't granted to higher-rep users (the ability to have a potential closure reviewed straight by a moderator). The third outcome above would thus never occur, and so recommend closure flags could never be marked declined. So SE simply changed the system so that a negative community review consensus would marked the flag as declined rather than disputed.
Also consider that the flag dismissal behavior varies for both flags: in the case of "very low quality" and "not an answer" flags, the actual review consensus outcome is checked, and the flag isn't dismissed until the whole review is complete. So if the flag outcome is disputed, it merely means that the overall consensus was that it Looks OK, but it's possible that some people recommended deleting it.
On the other hand, however, a recommend closure flag will only be marked declined if there is a unanimous vote against closure; as soon as someone votes to close (even outside of the review queue), the flag will immediately be marked helpful regardless of the review outcome. So a declined flag means that your flag was universally disagreed upon, not merely that the outcome was to leave it open (but possibly some people voted to close).