Noninvasive exam. A chest ct is very quick. You are passed through a doughnut shaped machine. They may give you a fluid (contrast dye) through a vein but many chest ct exams are done without dye. Mri takes more time and the machine is tube like in nature. They may also give you a fluid into the vein. Both are not painful without any recovery. Can be done in hospital or radiology practice office.
Computerized section. Both MRI and ct mean getting sections of your body with the aid of computer. Only difference is in "how". Ct uses x-rays and MRI uses radiowaves in a magnetic field. You lay still inside a machine which lookd like a short tunnel (gantry) and these enregies (x-rays or radiowaves) go through your body and records the density of your tissue. The computer analyzes the density and display image.