Diffusion: Imagine someone having perfume in her clothes entering a room and taking a seat close to the door while you are sitting on the opposite corner of the same room. Eventually, you are able to smell that perfume. This is due to the mixing of the perfume particles with air particles. However, it takes a while for you to be able to smell in spite of the fact that the molecules of the perfume travel very fast (hundreds of metres per second). This is due to the presence of other molecules of air in the room with whom perfume particles collide before reaching your nose.
Effusion: Suppose, now we remove all other molecules - that is, we have vacuum - then, perfume particles are able to travel much faster. Effusion is the process of gas particles going through a hole into the vacuum and effusion takes place much more rapidly than diffusion since in effusion, collisions with external gas molecules are not involved.
Graham's law is more accurate for the effusion process and is approximately correct for the diffusion process as there are different gases involved in diffusion process.