<p>There's nothing to directly explain the discrepancies between series, but from what I've seen, I think it comes down to the difference between simply manipulating an element and "bending". In the time of the lion turtle cities, people were able to manipulate the elements, but it was very simple and unsophisticated, simply referred to as "the power of (insert element here)". When Wan came around, he took that elemental manipulation to a new level, much more similar to the bending we know today. Thus, I think the term "bending" originally referred to advanced manipulation of the elements, and simply took a different meaning (namely elemental manipulation) as time went on. When people "learned" bending from the animal or celestial teachers, they didn't acquire the ability to manipulate the elements, but rather the advanced techniques that allowed for greater power and flexibility.
</p><p>Also, I'm fairly sure Toph was born an earthbender, like every other bender in the series. She simply acquired the ability of "seismic sense" from the badger moles.
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