What is the difference between lead, leading, and leadership?

Lead is a
present tense verb and it means to guide or direct in a course of
action.  Leading is the gerund of that verb, which
essentially acts like a noun in a sentence when combined with "is" or "am."  Example: I
am leading a group of scouts on a hike.  "Leading" here is an action but when combined
with "is" you should think of it more like an "activity."  What are you doing? 
Leading.  Leadership is a noun.  It is the
quality or characteristic of being able to
lead, or the capacity to do so.