A buildup is the pressure rise after a producing well is shut in. A drawdown is the pressure fall while it flows at a known rate. The interpretation uses the shape of the pressure and its derivative, not a single shut-in pressure. Permeability comes from the level of the derivative; skin comes from the separation between pressure and derivative; a boundary shows up as a late change in slope.
A test sees only as far as the pressure disturbance has travelled. A short test on a low-permeability well cannot prove a large connected volume. The radius reached in the test is a radius of investigation, not the drainage radius of the well.