Both would be deals with the Celtics. The Spurs know you don't trade an All-NBA caliber player without getting an All-NBA caliber player in return. So it comes down to this:

Spurs get: Kyrie Irving+2019 1st Rounder (Grizzlies)
Celtics get: Kawhi Leonard

Both will be free agents after next season. Boston doesn't necessarily want to occupy most of its cap space with Kyrie, and he's already expressed that he'll pursue the biggest deal he can get in free agency. The Spurs want a star they can lock-in for the long term, and by getting Kyrie this offseason they could offer $80M more in 2019. Meanwhile, the Celtics would be trading one expiring contract for another, but they'd get the better player. And perhaps Danny thinks a year in Boston could sway Kawhi to re-sign after this season.

The other trade scenario (though its very unlikely Boston would go for it):

Spurs get: Gordon Hayward & Jaylen Brown
Celtics get: Kawhi Leonard

This is the classic NBA trade where (when dealing with a superstar) $1 = $1.50 because you aren't getting a superstar in return. If the Celtics view the Kawhi-Kyrie-Tatum group as their future (Leonard/Irving are both 26), Hayward & Brown are expendable. And with all the draft picks Danny has accumulated, he can fill out the rest of his roster with cheap home grown talent over the next few years (they've got 7 1st Rd picks in the next 3 years). And there's no question the Spurs would jump at this deal as both Hayward & Brown would be under team control until 2021, while Kawhi has indicated he already has one foot out the door.