By respiratory system we usually mean the passages that transport incoming air to the lungs and to the microscopic air sacs called alveoli where gases are exchanged. The term respiration refers to the whole chain of processes from the inhalation of air to the use of oxygen in the cells. Index. Reference.
Phagocytes are the white blood cells that protect the body by eating (phagocytosing) dirt, bacteria and dead or dying cells. They are important for fighting infections. They are also important for becoming immune. Phagocytes are important in all animals and are very complex in vertebrates.
Monocytes share the vacuum cleaner (phagocytosis) function of neutrophils, but are much longer lived as they have an additional role: they present pieces of pathogens to T cells so that the pathogens may be recognized again and killed, or so that an antibody response may be mounted.