Crowley's special due to the large number of souls that he controls. Souls grant power in the Supernatural universe, and the ones in hell have granted Crowley various abilities that regular demons lack. For example, we've seen Crowley teleport, which demons aren't able to do. However, he still seems to be a demon deep down, as he seemed genuinely concerned at the threat of his bones being burned. In addition, holy water burns him like regular demons. And we've seen him trapped in Devil's Traps numerous times. Due to his power, he seemingly never has need to flee his body, which is the usual reason demons possess others.
Interestingly, a few days after you asked this, we see Crowley use his demon abilities. In Supernatural S8E2, he possesses Kevin's mother. Several things to note about this. First, before she could be possessed, her demon-warding tattoo had to be removed, which means Crowley's unable to possess people who have those. Second, he revealed himself by displaying dark demon's eyes, but his were neither black nor yellow, they were red, which we've seen before with another crossroads demon flashing red eyes in S2E8. Third, when he exited the body, he wasn't the usual black smoke, he was red-tinted (he also fled in smoke form back to his usual body). The previously-mentioned crossroads demon from S2E8 was regular black in smoke form, so the red color seems to be Crowley-specific.
It's possible that Gavin, as a ghost, was able to see Crowley's real face instead of his physical face that we the audience see. We know that other non-human beings are able to see demons inside people (e.g. angels and prophets have shown this capability), but what they see hasn't been clarified beyond it being monstrous.