The first Marvel character "Spider-Girl" was May "Mayday" Parker, a superhero in Marvel's MC2 Universe, where she is analogous to Spider-Man. (1998-2008)
The second Marvel Spider-Girl (nee Araña) is Anya Corazon, who had a crossover role in MC2 as well as appearances as an historically earlier Spider-Girl.
The DC character Spider Girl (no hyphen) was Sussa Paka, a 30th century member of the Adult Legion of Superheroes and the group Workforce. She was also known as Wave, and had prehensile red hair.