A hug was a social expression which generally involved one or more individuals fully embracing others.
The Ninth Doctor once voiced an affection for hugs, claiming he would hug anybody, (TV: The Long Game) and gave them out to comfort others, (TV: Father's Day) or when in moments of joy. (TV: The Doctor Dances, Boom Town, Bad Wolf)
In contrast, the Twelfth Doctor held a strong distaste for hugs as they made him feel uncomfortable, (TV: Deep Breath) protesting to Clara Oswald when she attempted so that he was "against the hugging." (TV: Listen) This incarnation of the Doctor would, however, voice that hugs were a good way to smell someone's hair as he hugged Clara to comfort her after she was almost shot. (PROSE: The Blood Cell) The Doctor explained to Clara his belief to "never trust a hug", claiming it was "just a way to hide your face." (TV: Death in Heaven)
Hiding the loss of Danny Pink, Clara concurred as she hugged the Doctor before parting ways. (TV: Death in Heaven) After reuniting, the Doctor began to accept Clara's attempts to hug him over time, (TV: Last Christmas, The Woman Who Lived, Face the Raven) and even started hugging her on the odd occasion. (TV: The Magician's Apprentice, The Girl Who Died) By the time he reunited with Maxwell Edison, the Doctor had accepted being a hugger and gave a loving hug to Max. (COMIC: The Stockbridge Showdown)
The Twelfth Doctor, Bill Potts and Nardole shared a group hug, which Nardole called a cuddle, when he joined in on Bill's hug with the Doctor, when she discovered she was still alive. When Bill earlier hugged the Doctor, on finding out he was blind, he urged her not to "get all gooey on me", as he claimed it was a temporary condition. (TV: Oxygen)