What is the difference between the stage and the grade of lung cancer?

A lot. Stage refers to extent of cancer: generally stage 1 & 2 are early cancers; stage 3 involves spread to the nodes or structures in the middle of the chest; stage 4 involves spread to both lungs or other organs. Grade refers to the degree of abnormal appearance of the cancer when seen under the microscope- usually grades range from 1-3.
Refer to diff things. Stage refers to the extent of the disease. It includes the size of the tumor (t stage), whether lymph nodes are involved (n stage), and whether it has spread to other sites of the body (m stage). The tnm stages are put together to give an overall stage of i-iv. Grade refers to what the tumor cells look like under the microscope and are usually graded as low, intermediate, and high.
Difference. Stage refers to the size and invasiveness of a tumor (t) involvement of lymph nodes (n) and evidence of metastasis (m). Grade refers how organized or differentiated a tumor is as it looks underneath a microscope.