You are confusing terms. What you see are tiles being rendered by default blender doesn't render the whole image but it renders it in tiles to maximize the resources on your computer. Your machine is using 8 threads to render (two threads for each core on the CPU). The size of those tiles is determined in the performance tab:
By default blender uses auto-detect to determine how many threads to use for rendering, or you can choose to use a fixed number. If you render using GPU you will have as many tiles as GPUs you have installed in your machine.
Read: How do the number of cores in the CPU relate to the rendering tiles?
Read also: How can I render the way the render preview renders?
The square sample box does something completely different. It has nothing to do with the shape of the samples. When you enable "square samples" you are mulitplying the number of samples by itself.
