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Paladins are completely separate from the other two, and are a defender wearing plate/shield, who focuses on defending allies and can choose either STR or CHA based powers.

Clerics (including warpriests) are leaders, meaning they have access to healing powers and powers that buff allies or hinder enemies. Initially clerics had primarily wisdom-based implement or strength-based weapon powers, but the Warpriest shook things up a bit by adding a slew of wisdom-based melee powers. The Warpriest also gets shield proficiency for free, but doesn't get to pick its powers (its domain/diety choice determines its power selection at all levels).

The Warpriest (like all essentials subclasses) is meant to be a fast/easy to build/play option, while the traditional cleric offers a wider array of options.

Its tricky because they used the word warpriest in multiple ways and built the cleric class over a couple of years.  And cleric now has more sub builds and I think powers than any other class. 

Every cleric starts out as a warpriest or a templar (the PHB version you have).  You have a DDI subsciption so you can look up all the specific differences in the compendium. 

Templars use strength and wisdom for their attacks.  They can pick from any cleric utility or attack power with a level.  They have both weapon and implement attacks.  Templar weapon attacks are roughly evenly divided between strength and wisdom, but almost all implement attacks use wisdom.  A tiny handful of powers let you pick either strength or wisdom.

Warpriests use wisdom for their attacks.  There are 9 domains to pick from when you pick warpriest.  They don't pick their at wills or encounter powers, but have them automatically assigned to them based on which domain you pick.  So a Sun domain warpriest will have a completely different set of at wills and encounter attack powers than a Storm domain warpriest.  8 of the 9 domains are only assigned weapon powers, but the death domain is assigned only implement powers.  All warpriests get a few assigned channel divinity and utility powers, some of which are the same for all warpriests and some of which vary by domain.  Warpriests can pick from Templar leveled utility and daily powers, so its common for warpriests to pick up templar implement daily attack powers since those tend to be better than the weapon dailies.

The word "warpriest" is also used in two paragon paths.  All clerics can pick the "Tactical Warpriest" paragon path,  Only Warpriests can pick the "Devout Warpriest" path.

There is a cleric handbook and warpriest handbook in my signature that go into a lot more detail.