Dear student.
No, they are not same.
B lymphocytes develop into memory B cells after activation by antigen interaction. These cells are able to live for a long period of time, and can respond quickly if a person is exposed for the second time with the same antigen. So B cells develop a memory for a particular antigen which protects us from the attack of the same disease again and again.
Memory T-cell is a subpart of T-cell, they are also known as antigen-experienced T cell, because of the previous interaction with an antigen. It is of two types: central memory and effector memory T cells. Central memory T-cell remains present in lymphoid organs and bone marrow, whereas effector memory T cells remain in peripheral tissues
Regards.