Forced vibration:
The object oscillating will vibrate upwards and downwards with the same frequency the driving oscillation is at. The amplitude of the vibration increases as the frequency decreases and there will be a phase difference between the driving vibration and the forced vibration. When the driving frequency is much greater than the forced frequency then there is almost a 180o phase difference, however when the driving frequency is much less than the forced frequency, then there is almost no phase difference
Resonance:
The frequency of the vibration is the same as the naturual frequency of the system. The rate of energy transfer from the driving force to the system is at a maximum and so the amplitude of the resonance is very large. The driving frequency is either 90o ahead or lags by 90o.