In the lines 8-12 of "A child said...", he can't provide an exact definition of the grass, as he knows it no more than a child does. But he can say one thing for certain: the grass doesn't discriminate between different people. It grows everywhere, among blacks as well as whites, in different places of the world.
In the lines 14-25 of “I understand the large hearts….” Whitman doesn't just sympathize, but identifies with all the oppressed - a woman who was burned for allegedly being a witch, a hounded slave who was tortured. He says "All these I feel or am". So, he has more than empathy for his fellow creatures, no matter what their circumstances were, or their fate.