The answer to this question can be usefully linked to the key theme of freedom from the restrictions of society, which is of course a vital element in Thoreau's teachings. Note the way that so many characters show that they are just living their lives rather than consciously "being," or "living deliberately," as Thoreau might have put it. Consider the way that dialogue is used to demonstrate this, especially through the words "get along" and "go along," which are used at various points to indicate that you should just "go along" unprotesting with the force of society rather than protesting against it and "walking to the beat of a different drum." Note how Bailey responds to Henry's desire to complain about how Bailey has been waiting for so long for his trial:
I don't want to make a ruckus. I'm not a troublemaker. I just want to earn my keep, make a little tobakky money, and get along.
Bailey is a perfect example of a character who is just living his life, rather than actively being, whereas Henry, by contrast, shows be is determined to be rather than simply live in the response he gives to Bailey:
"Get along!" Those words turn my stomach.
So many characters in this play "go along" with society and its dictates, showing their inability to challenge society and make their own life in opposition to it as Henry is so obviously determined to do. The difference between living and being therefore is based around merely letting ourselves and our dreams being ruled by life, and remaining passive, or resolutely being determined to be active in our lives, refusing to just merely "live," but to actually "be."
I think that Thoreau defines "living" and "being" in terms of one's commitment to a belief system or set of values. Consider the opening when Thoreau questions the mere order of the alphabet. This is an instant where Thoreau believes that life is merely more than "being," a condition in which individuals blindly accept what is in front of them without questioning what can be or what should be. In reexamining the order of the alphabet, Thoreau demonstrates what he considers "living" to be, a form of consciousness where individuals actively partake in the world in which they live by transforming what is into what can or what should be. This becomes the difference between "living" and "being" in that the latter is an active engagement and participation with consciousness, while the latter is more receptacle- like and passive. This becomes highlighted in Thoreau's stance on the war, an issue in which "being" indicates passive acceptance of a condition that Thoreau believes in fundamentally wrong. In this light, Thoreau defines "living" as a state where individuals voice dissent. If one does not do so, Thoreau believes that a major component of human existence is lacing, resulting in life as simply "being" and not one that is rooted in "living."