Captain Michael Burnham (Sonequa Martin-Green) in Star Trek: Discovery and Worf (Michael Dorn) in Star Trek: The Next Generation have some key similarities, but the biggest thing they have in common no longer matters to their respective stories. Both Burnham and Worf were orphans who were raised by parents from alien cultures; Michael was raised by the Vulcan Ambassador, Sarek (James Frain), and his human wife Amanda Grayson (Mia Kirshner), while Worf was raised by Human foster parents Sergey (Theodore Bikel) and Helena (Georgia Brown) Rozhenko. Their blended upbringings gave them unique insights into both their native and adoptive cultures.
For example, when Worf left the USS Enterprise-D to fight for the Klingon Empire in Star Trek: The Next Generation season 4, episode 26, "Redemption", Captain Jean-Luc Picard (Patrick Stewart) noted the Klingon's humanity as one of his strengths. Worf's TNG Klingon Empire problems were often rooted in the clash between his loyalty to the Federation, and his loyalty to his own species. Michael Burnham also had a complicated relationship with the Klingon Empire, and it was how both Burnham and Worf dealt with their Klingon problems that connect the two characters across the centuries.