In tennis a ball in in if hits any part of the line. In squash, the ball is out if it hits any part of the line.
In Australian football a player can play the ball whilst out of bounds as long as the ball is not totally over the line. In rugby (and American football I think) a player with the ball is out if he steps on the line.
Are there consistent clusters of sports? When the rules for these games were codified, did no-one look to see what other sports did? Or is there some hidden compelling reason to be the way it is in each sport?
Why would you expect them to be consistent? They were developed by different people at different times, and sometimes in different countries. Someone had to arbitrarily decide what would happen if someone touched the line, so they went with whatever the felt like.
In basketball, on the line is out of bounds.
In baseball, on the line is fair.
In ice hockey, the puck has to go completely across the line for a goal (as it does in Association Football.)
However in Association Football, the player can be out of bounds (touch) while playing a ball that is in bounds (touch).
The differences probably arose throughout the years as rulesmakers decided which would be fairer for the particular sport and which would be easier for officials to call.
Association football (I’m just trying for a lingua franca here) seems to have the primary goal of avoiding having play stop.