Meaning:

• Sun was shining bright. We went for a walk.
• Sun was shining bright; we went for a walk.
• Sun was shining bright, and we went for a walk.
• Sun was shining bright, so we went for a walk.

In the first example, the two sentences are independent expressions, while the last is that of dependence. However the connection of thought in the first examples is just as real as in the last ones, where it is explicitly expressed via the syntax of subordination. In fact, the putting side by side (without any indication of a separation, e.g., of a pause) of two totally nonrelated sentences usually startles the listeners, who try to figure out whether the train of thought was lost for them. This arrangement is either an indication of a mental disorder of the narrator or of humor (similar to garden path sentence).