Terry Newell proposed the following model, illustrated below, in his 2012 book entitled
Statesmanship, Character, and Leadership in America. Briefly, Newell's model includes six different factors which make up the overall quality of statesmanship. He argues that none of the six factors is more important than another - "There is no order
of precedence; the leader moves among the six factors with dexterity
in aiming for an act of statesmanship."
Firstly, the political context in which the leader's actions are taken, secondly, the leader's character, which combines a multitude of factors such as self-criticism, virtue, and, indeed, leadership.
The next three factors are sets of skills which Newell expects every successful statesman to master. These are shown in the three segments surrounding the centre of the diagram below: a transcendent purpose, a mastery of the art of politics, and an ability to persuade and compel support. He calls up visions of, for example, Martin Luther King Jr.'s ability to "command the nation’s attention from a jail cell because he
could reconnect us to the purpose of America."
Finally, Newell argues that the last component is an aspiration to shape the nation's character: "Unless people rise
to the leader’s moral vision, statesmanship is glorious in the attempt
but remains, in Langston Hughes’s words, a 'dream deferred.'".
While Newell's model particularly examines the American view of statesmanship, hopefully that helps you separate the two terms in a more abstract context.