Drift and diffusion
A common SDE has the form
\[dX_t=a(X_t,t)\,dt+b(X_t,t)\,dW_t.\]The drift \(a\) describes the systematic local direction of change. The diffusion coefficient \(b\) controls the magnitude of random fluctuations.
Over a small interval,
\[\Delta X\approx a(X_t,t)\Delta t+b(X_t,t)\sqrt{\Delta t}\,Z.\]Key idea. Drift represents systematic change; diffusion represents random variation around that change.