Castiel and Zachariah (and possibly Naomi) are Seraphs. Michael, Gabriel, and Raphael (and possibly Lucifer) are archangels while everyone else is a regular angel.
But Gadreel is not a regular angel obviously. Castiel is a seraph and he said that even HE can't heal Sam's trial injuries. But that possibly was because he was weakend from purgatory a tiny bit. Gadreel was able to heal most if his internal burns although the fall weakened him. But he said he will heal himself while healing Sam. I'm willing to bet thaft Gadreel is either a seraph or one of Naomi's type.