Cunningham is averaging 5.0 points and 3.8 rebounds in 51 games this season, while Vaughn has produced 2.6 points per contest in 22 games with the Milwaukee Bucks and one with the Nets.
The 30-year-old Cunningham is a nine-year veteran who has enjoyed stints with the Portland Trail Blazers, Charlotte Bobcats, Memphis Grizzlies, Minnesota Timberwolves and Pelicans.
He seemingly found a home in New Orleans, as he spent the past three-plus seasons with the Pels.
Cunningham alternated between starting and coming off the bench for New Orleans, and so far this season he has made 24 starts.
In 629 career NBA regular-season games, Cunningham averages 6.0 points and 3.8 rebounds per contest.
Vaughn, 21, is in the midst of his third NBA season.
The Bucks selected him with the No. 17 overall pick in the 2015 NBA draft out of UNLV before dealing him to Brooklyn on Monday in a trade that sent center Tyler Zeller to Milwaukee.
Vaughn has struggled to find consistent playing time at the NBA level, and in 134 career games, he averages just 3.1 points and 1.1 rebounds.
Both Cunningham and Vaughn can become unrestricted free agents this offseason.
Cunningham will likely serve as a primary backup to forwards Rondae Hollis-Jefferson and DeMarre Carroll in Brooklyn, while Vaughn will provide depth behind the backcourt duo of Jrue Holiday and Rajon Rondo in New Orleans.