The Knight and Slayer fighter builds are presented in separate sections of Heroes of the Fallen Lands, and have very little in common. They have different armor proficiencies, different powers and even different roles. Here’s what they share:
Of the at-will stances, Slayer and Knight share Battle Wrath (+2 to damage) and Poised Assault (+1 to attack).
Both Knights and Slayers get the Power Strike encounter power feature.
Of the Level 2 utility powers, Knight and Slayer share Minor Resurgence (gain 5 temporary HP when bloodied) but the other 3 choices differ. (Since all these utilities are labeled “Fighter Utility 2”, can a Knight take one from the Slayer section and vice versa?)
For the most part, Knights and Slayers get different class features. For example, at Level 4, Knights get +2 to initiative, while Slayers get the ability to draw a weapon as a free action.
Knights and Slayers seem to diverge about as much as possible and still be part of the same class. Although this approach has potential pitfalls, I much prefer it to the needless multiplication of basic classes. There’s no way, for instance, that the Cleric and the Runepriest should be separate classes.
I’m pretty sure that these builds and the fighter from the phb all share utilities and that Mike Mearls has stated as such in the past. HotFL doesn’t make any mention that you can choose different utilities than the ones they present, but I think that’s more for the sake of simplicity than anything else. It makes sense that Wizards would want their essentials books to feel a little self contained rather than overwhelming a player with constant references to other books and powers.