So when the cleric class has a header section called "Class Features" and under that is an entry that says "Channel Energy," and the oracle class has a section called "Class Features" and under that is an entry that says "Channel: You can channel positive energy like a cleric," and the paladin class has a section called "Class Features" and under that is an entry that says "Channel Positive Energy (Su): ... she gains the supernatural ability to channel positive energy like a cleric," those all are intended to work the same way, even though they're not given identical names. For one, because the paladin and oracle "versions" of that ability tell you it works like the cleric "version" of the ability. For two, because having them all work the same way is simpler and easier to remember than each of them working a different way. Now, given, the oracle gets 1+Chamod per day instead of the cleric's 3+Chamod, and the paladin spends uses of lay on hands instead of a separate X/day allotment, but if you line up a good cleric 5, a life oracle 5, and a paladin 5, and tell each of them to channel a burst of positive energy, all three of them are healing 3d6 to living or dealing 3d6 to undead, DC 10 + 1/2 level + Chamod, 30 ft. radius, no AOO, and so on. Exactly the same. Because it's easier to remember that way. Because it makes the game easier to run that way.
And that means things like Improved Channel and Alignment Channel and Extra Channel should apply equally to the cleric, life oracle, and paladin (you'll note for Extra Channel the paladin ability's counting method of uses per day for the feat is slightly diff because the paladin ability is based on using lay on hands, but the net result is the paladin gets +2 uses of channel per day, just like the cleric and oracle). Because to do otherwise means we need different versions of these feats for oracles and paladins because under the strictest interpretation, neither of them has a class ability that's specifically and explicitly named "channel energy;" and three sets of redundant identical feats for clerics, oracles, and paladins is lame and a waste of space.