Final answer:
B cells complete their maturation in the bone marrow, whereas T cells mature in the thymus.
Step-by-step explanation:
B cells complete their maturation in the bone marrow. These cells, which originate from stem cells in the red bone marrow as part of the adaptive immune system, undergo a development process where they learn to distinguish self from non-self. Post maturation in the bone marrow, B cells journey to the circulatory and lymphatic systems to engage in the immune response. T cells, on the contrary, begin their journey in the bone marrow but mature in the thymus, a process crucial to ensuring the body does not mount an immune response against itself.