Regular non-capturing groups allow the engine to re-enter the group and attempt to match something different (such as a different alternation, or match fewer characters when a quantifier is used).
Atomic groups differ from regular non-capturing groups in that backtracking is forbidden. Once the group exits, all backtracking information is discarded, so no alternate matches can be attempted.
A possessive quantifier behaves like an atomic group in that the engine will be unable to backtrack over a token or group.
The following are equivalent in terms of functionality, although some will be faster than others:
a*+abc (?>a*)abc (?:a+)*+abc (?:a)*+abc (?:a*)*+abc (?:a*)++abc