All white blood cells are indeed immune cells, but not all immune cells are white blood cells.
All white blood cells are immune cells. Not all immune cells are white blood cells

Functions of blood: its role in the immune system
Source: blood.co.uk
Key Evidence
Sources consistently describe white blood cells as integral immune system cells that fight infections.
urmc.rochester.eduurmc.rochester.eduWhat Are White Blood Cells?
blood.co.ukblood.co.ukFunctions of blood: its role in the immune system The immune system also includes other elements beyond white blood cells, such as proteins and organs involved in immunity.+3 more
What the Evidence Shows
White blood cells (WBCs), also known as leukocytes, are a key component of the immune system and are primarily responsible for defending the body against infections and foreign invaders. Multiple sources confirm that white blood cells circulate in the bloodstream and tissues to identify and attack pathogens.urmc.rochester.eduurmc.rochester.eduWhat Are White Blood Cells?
blood.co.ukblood.co.ukFunctions of blood: its role in the immune system+2 more
However, the immune system is broader than just white blood cells; it includes other components such as proteins (e.g., antibodies), organs (e.g., bone marrow, thymus), and chemical signals that contribute to immune defense.my.clevelandclinic.orgmy.clevelandclinic.orgImmune System Function, Conditions & Disorders
healio.comhealio.comComponents of the Immune System
Therefore, while every white blood cell functions as an immune cell, the category of immune cells can extend beyond just white blood cells to include other specialized immune components and cells that may not be classified strictly as white blood cells. This distinction supports the statement that all white blood cells are immune cells but not all immune cells are white blood cells.