There are lots of different types of white blood cells and any one of them can turn leukemic. Back in the 1840s Rudolf Virchow didn't know this. Even now looking back we don't know what sort of leukemia his patient had. Actually, Rudolf was the first to describe leukemia. He was beaten to the punch by John Hughes Bennett, an Englishman working in Scotland, who published six weeks before Virchow. We don't know what sort of leukemia his patient had either. It wasn't until Paul Erlich learnt how to stain cells on a blood film that it became possible to distinguish different types of white cells.
The distinction between the two chronic leukemias was easily made, but the acute leukemias still looked very similar and it was many years before they could be distinguished using specially developed stains.
The abnormal cell in CLL is a small round cell containing a round nucleus that occupies most of its bulk, and a thin rim of unremarkable cytoplasm. The nucleus stains a uniform dark blue color with no visible features. Apart from saying it was a small lymphocyte there was not much more to be said, and even as late as the 1950s nobody was sure about what lymphocytes were there for. It gradually emerged that they were part of the immune system and by the 1970s it was clear that there were two major types. All lymphocytes are apparently made in the bone marrow, but many of them need further processing in the thymus, an organ in the front of the chest that is prominent in children but shrinks as a person ages. Such cells are called T-cells. Most of the rest of the lymphocytes need a different type of processing. In chickens this is done in an organ near the cloaca called the Bursa of Fabricius. Consequently, such cells were called B-cells.
Humans and other mammals don't have this organ and a lot of time was spent looking for a 'bursa-equivalent'. In the end they decided that all the processing of B cells takes place in bone marrow, which, luckily, also begins with a 'b'.
As time has gone by we have developed more and more sophisticated means of distinguishing one type of cell from another. The most useful technique involves staining with labelled monoclonal antibodies. This has been given the posh name of immunocytochemistry. The various monoclonal antibody targets have been given numbers preceded by the letters 'CD' which stands for 'clusters of differentiation'. Your probably no better off for knowing that.
CLL cells are B cells, but they have an unusual CD signature. They turn out to stain positively for CD5, CD19 and CD23. All B cells have immunoglobulin molecules on their surface, but CLL cells have only about one tenth of the normal amount. There are two other molecules that CLL cells have less than the normal amounts of: CD20 and CD79b. With such a distinctive signature you'd think it would be easy to find the exact normal cell that CLL is derived from. Unfortunately, there isn't one. At one time many people thought it was equivalent to the B1 cell in the mouse, but that cell lives in the peritoneal cavity of the mouse and there isn't really a human equivalent. Other suggestions have been memory B cells and marginal zone B cells, but in truth the peculiar CLL signature is not the same as that of any other cell that we have discovered.