Please note the JavaDoc never says "leash entity". It does refer to the "living entity's leash". Then if you are wondering what a "leash" is, you can look at the signature and see it is an Entity. If I meant LeashEntity then the signature would reflect that.

Also I don't think linking the two entities is the correct default behaviour, because when a player links itself to an animal, that link is only one way. There should always be a leader and a follower, otherwise LivingEntities movement will get pretty weird. But if you want to link two pigs together for example you still can :)