Body wash is the general term for liquid products used for cleaning your body.
e.g. Use a soft body wash or soap to clean your body.
A lotion is a liquid that you put on your skin in order to clean, protect or treat it.
A body lotion is a lotion that you apply to your body after bathing.
e.g. Regular use of a body lotion will keep the skin soft and supple.
A cream is a substance that you rub into your skin, for example, to keep it soft or to heal or protect it.
e.g. Treat your hands with a special hand cream.
e.g. Your skin does not look good recently. You’d better use facial cream.
e.g. Gently apply the cream to the affected areas.
A moisturizer is a cream that you put on your skin to make it feel softer, smoother and less dry.
e.g. Find a moisturizer that fits your skin type and makes your skin look and feel soft.