What kind of motion will an airplane enter into when disturbed?
The separation into short-period and phugoid motion is somewhat artificial. There is just motion. It just happens that when you fly a 'real' airplane (or solve its equations of motions), you'll have quite different timescales for angular motion (isolated pitch; low seconds) and linear motion (changes of altitude and speed; tens of seconds and even minutes).

Broadly speaking, heavier and faster airplanes with swept wings demonstrate more of this separation. At the other end of the spectrum, smaller airplane models have similar timescales for both the short- and long-period motion, and for them the separation is not meaningful (which makes it more difficult for analysis!)

So, to answer the question, both will usually occur. In some cases, depending on the airplane and your point of interest, you can ignore one or the other. On airplanes where separation is significant and motion is stable and well damped, it may also be possible to produce a disturbance that results in (practically) one kind of motion: either short-period (e.g. a small elevator impulse) or long-period (e.g. a brief application of pitch-neutral air brakes).