The 'Punk' subculture includes diverse ideologies, fashion, and other forms of expression, visual art, dance, literature and film. The subculture promotes freedom and individuality, they would typically wear dark clothes, ripped jeans etc. Their body language in pictures is quite aggressive and they like to make themselves look big and intimidating, for example as you can see the picture above they had coloured hair and had their middle finger up.
'Teenybopper' is a subculture which is where a young teenager, usually around the ages 13-16, follows adolescent trends in music, fashion and culture.
Most popular music artists nowadays name a group of their fans a name after them, also known as a stan, 'an overzealous or obsessive fan of a particular celebrity.' -Google dictionary. For this, I am going to focus on a band called All Time Low, who call their fans 'Hustlers' they have their own website where their fans sign up and pay monthly for a membership which entitles them to receive pre-sale tickets to their tours, priority meet & greet of the band and posters and goodies. All Time Low's fanbase is quite alternative, rocky and punk and normally their shows are very wild and crazy. For teeny boppers, Taylor Swift calls her fanbase 'Swifties' and they are very different to All Time Lows fanbase, most of her fans are younger and more into country/pop music whereas All Time Low's fan base as mentioned are 'punk' and are most likely to go wild at a gig, like mosh pits, crowd surfing and circle pits which wouldn't be very ideal for the 'Teenyboppers'.
Most of All Time Low fan base would dress dark and gothic, with the occasional coloured blue hair and piercings, more towards the 'punk' subculture and Taylor Swifts fan base would be usually wearing casual clothes, generally because most of them are younger, these facets pretty much define the 'teenybopper' subculture.