The two are shown to be very close to each another, especially with their Captain and Vice-Captain relationship. They are often seen interacting in regards to decisions for the team, and are usually the ones Coach Ukai comes to when having to deal with the team. Daichi and Sugawara are currently classmates in their third year.
Asahi is also a third year and is shown to be very in-sync with Sugawara on the court. Coach Ukai commented on their setter-spiker relationship as something that's been "built over time". The two's relationship were a little murky after the loss against Date Tech High (as seen in Chapter 20), but after a match with the Neighborhood Association, they patched things up.
Sugawara acknowledges Kageyama's ability, calling him a "talented first year setter", but is still unwilling to "give up" the position of setter to him. He does, however, let Coach Ukai understand that his feelings will not be hurt if he isn't playing as a regular, and he continues to treat Kageyama as a junior that he could both teach (especially in regards to interacting with the team) and learn from. Sugawara is also shown to be Kageyama's "handler", mostly in the early chapters where he's given the task to calm Kageyama down.
Yaku and Sugawara have similar personality type, and are seen conversing in a friendly manner on multiple occasions.
They first met during the Nekoma vs Karasuno practice match when Taketora and Tanaka were causing trouble. Sugawara and Yaku apologized to each other for their teammates and soon bonded over their similar positions of being caretakers for their teams.