A wireframe is a 2d illustration of a page's interface that specifically focuses on space allocation and prioritization of content, functionalities available, and intended behaviors. For these reasons, wireframes typically do not include any styling, color, or graphics.
Layout is defined as the arrangement of predetermend items on a page. Basically, you're given the pieces and they are arranged. Design is defined as the art or skill of combining text, images, and other items into a visually pleasing arrangement.