The battlemaster controls the battlefield and knows his enemies.
The Champion is a master of his weapons and a tough motherfu***.
And other people will find other essences for the classes. Really, there is no problem.
Its because you have read the PHB though. I think its more for new players or in 4E and 3E with some of the PrCs and class names were WTF.
Whats a seeker, warden, Dragon Disciple for the uninitiated for example? A fighter, assassin, wizard means something even if you have never played D&D before. What is a Duskblade?
Zardnaar nailed it.
5e has mostly moved away from the tendency of later 3e and most of 4e to create character concepts defined mainly mechanically. EDIT: In an ideal world, the mechanics and narrative positively reinforce one another, and that's what 5e aspires to do with most of its class design.
However, the fighter is an exception to that trend.
Now, for people who would prefer a "class-less" D&D or a flavor-less "class-lite" D&D, they love that the fighter is designed how it is. Nothing wrong with that. But it is a glaring exception to how the rest of the 5e classes are designed.
What sticks out as a sore point is for people who are more casual gamers or newer to the game being unable to readily differentiate Champion vs. Battle Master, whereas they quickly grok the difference between a Thief vs. an Assassin. And even once they have the rules down enough to understand the mechanical difference between Champion vs. Battle Master, they still have no narrative distinction between these two subclasses.
IMO, it's not that players need a straight-jacket to tell them "here's your PC's pre-packaged story," rather it's that the human mind goes toward identifiable archetypes as a starting point, that creativity is MORE inspired by having a clearly understood springboard to launch from.
Mike Mearls' quote nailed it to me:
Champion is empty calories. There's no inherent meaning in the name. There's no implicit narrative creative springboard for players to work with. For a veteran/hardcore gamer, that may not be a problem (or even an advantage). For a newer/more casual/more story-focused gamer, that may be a problem.