Final answer:
Isis King was the first transgender model to compete on America's Next Top Model, while Laverne Cox is known for her acting and advocacy, but not for participating in that show.
Step-by-step explanation:
The first transgender model to compete on America's Next Top Model was Isis King. Although Laverne Cox is a highly recognized transgender actress and advocate for LGBTQ issues, known for her work on the television series 'Orange Is the New Black' and for her speaking tours like "Ain't I a Woman?", she was not a participant in the modeling competition.
Carmen Carrera is another well-known transgender individual who has gained fame after appearing on reality TV and is also a prominent advocate for transgender rights. Andreja Pejić is a significant name in fashion as a transgender model but never competed on 'America's Next Top Model'.