I don't believe they are closely related, but they're habits are fairly similar. They're both diurnal snakes that feed heavily on lizards, and they both hunt them out rather than ambush and wait for them.
Yup. Patchnose are almost strictly lizard eaters. They're diurnal, fast, and have great eyesight. They're hunters, so they actively forage looking for lizards and chasing them down instead of posting up somewhere and ambushing.