I'm not sure where you read that but it's not true. A few blood types, such as B cells and activated T cells, actually divide very rapidly under the right circumstances. What most people think of as "white blood cells" are macrophages, and those in fact do NOT divide.
"White blood cells" is just a general term to describe cells of the immune system. It's name comes from when you centrifuge blood and three layers are formed. The plasma forms on top (looks yellowish), the immune cells are in the middle (looks whiteish) and the red blood cells are at the bottom. Therefore it includes a wide range of cells with many different roles.
"Leukocyte" is just another name for "white blood cells", and ALL blood cells come from hematopoetic stem cells, so I'm not sure why that was mentioned in the above post.