A "bugtwink" is any effeminate korean male, typically spammed by adolescent sexually confused overweight k-stans on their tenth twitter handle. The "bug" portion in relation to them all looking alike.
A buttwink is when a person flexes their anal sphincter, causing their anus to visibly contract, effectively "winking" with their asshole. Buttwinking can be performed as an obscene gesture, or in a sexual context it can be either a sign of affection or a greeting.
To buttwink, simply use the same muscles used to defecate to flex your anus.
This act should not be confused with mooning (merely exposing your anus) since buttwinking is considerably more rude.
As Sensei Doug walked to his dojo, the rude employees of a strip mall store lowered their drawers, pointed their behinds towards the window, and contracted their assholes to buttwink at the passing martial artist.
Miguel: Did you like Superbad?
Carlos: Yeah dude it was sweet except the bloody jeans part was sick.
Moberry (From out of nowhere): Who has bloody jeans?
Miguel and Carlos: Moberry you're such a damn buttinsky.
Buttwings are small wings that can be found on the rear-end (butt) of something; they are generally found on non-existent things like Victini and anything that's free to buy.
Victini has a pretty prominent, but small pair of Buttwings that allow it to fly around and cheat the laws of physics.
When your "brown eye" (also known as an anus hole) contracts, which causes a closing effct. Once the anus hole opens once more its ends the completion of the "buttwink".