There is no one relationship between Hal and Falstaff. Rather, there are several.
Falstaff fills the position of surrogate father, and one a lot less scary than Hal's real dad.
Hal and Falstaff are drinking buddies; they enjoy wasting time together.
Falstaff is a way for Hal to get access to not just the lower classes, but the riffraff of society (thieves, prostitutes, etc.). This is both a kind of slumming and a kind of education for the future king.
Finally, Falstaff is a kind of dark mirror. Hal wants to shrug off the burden of honor, but he sees in Falstaff the results.
They are friends. Falstaff is a clown, and Hall is a young, younger man amused by him. By today's standards you'd say Hal was a follower of Falstaff. Hal looks up to him.
The relationship between the both of them are very close. They trade barbs, showing their equality to each other. They are very unseperatable buddies as they always hang out with each other and enjoy spending time, but one thing that seperates the two of them: Hal is Falstaff's superior in ranks and positions and in moral courage from the very start of the story