Cytotoxic T cells are known to be CD8+. CD markers are surface proteins used to identify immune cells. The function of cytotoxic T cells is to directly kill the antigen infected cell by releasing certain cytotoxic substances in the cell which include granzyme and lysozyme. Cytotoxic T cells recognise MHC class 1 molecules that act as antigen presenting cells for the CD8+ cells. 

Function of Cytotoxic T cells

Helper T cells are known to be CD4+. Their basic function is to produce cytokines that up regulate the immune system and alert the other phagocytic cells. Helper T cells can be further divided into TH1, TH2 and TH17 cells. TH1 cells stimulate the CD8+cells and macrophages to kill the infected cells.TH2 cells stimulate B cells to produce antibodies. TH17 cells help maintain the mucosal barrier and is involved in auto-immunity. They are also involved in pro-inflammatory response as they recruit neutrophils and macrophages to site of infection. T helper cells recognise MHC class II molecules.

Function of Helper T cells

Regulatory T cells are CD4+,CD8+ and FoxP3+. The basic function of these cells is to down regulate the immune system. These cells are important for the "self check mechanism" to prevent auto immune diseases. 

Function of Regulatory T cells

T lymphocytes, which are commonly called T cells, express T cell receptors (TCRs) on their surface.  These are transmembrane proteins that bind to processed antigens that are presented by antigen presenting cells (ATCs).  
There are three types of T cells, differentiated on the basis of their functions:
1. Cytotoxic T- cells
2. Helper T cells 
3. Regulatory T cells

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State University of New York at Buffalo

The common lymphoid progenitor matures into four mature categories of lymphocytes:

- B lymphocytes
- natural killer (NK) cells
- NK-T cells
- T lymphocytes

Common Lymphoid Progenitors

Chaplin, D. D. (2010). Overview of the immune response. Journal of Allergy and Clinical Immunology, 125(2), S3-S23.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2923430/
doi: 10.1016/j.jaci.2009.12.980

Overview of the Immune Response

B lymphocytes, which are commonly called B cells, express surface B cell receptors for antigen immunoglobulins.  B cells are further differentiated based on which kinds of antigens they respond to and which type of antibodies they produce. There are two different types of B cells:
1. Plasma B cells
2. Memory B cells

B Lymphocytes

T Lymphocytes

Natural killer (NK) cells are large mononuclear lymphocytes that target abnormal cells, including virus-infected and cancerous cells, and lack either T cell receptors (TCRs) or surface immunoglobulin (Ig). Abnormal cells do not express the normal major histocompatibility complex (MHC). Normal MHC markers prevent NK cell activation, so abnormal MHC expression by abnormal cells recruits NK cells (signals cell distress). Binding of NK cells on target cells (and detect abnormal MHC levels) also leads to activation. After activation, NK cells can employ several mechanisms for target cell destruction.

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Natural Killer Cells

Natural Killer (NK)-T cells are lymphocytes that share the characteristics of both NK cells and T cells.  

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