Phase Difference
Phase is the relative position in the cycle.
Each time that the process attains the same position its phase will have advanced 360 degrees.
Take as periodic process as a walking person, and place the start of phase when the right foot touches the earth. When the phase advances 180°, the left foot touches the earth. When the phase advances 360°, the right foot touches the earth.
Now take two persons walking beside. They start touching the earth with their right foot simultaneously: they are in phase, their phase difference is zero.
If they are parading soldiers they will stay in phase and their right foots will continue to touch the earth simultaneously.
But if they are not parading, the pace period of each one will be probably different. If the period of person B is shorter, his right foot will touch earth a little before person A. We say that person B is in advance on phase relative to A. Or that phase of A lags B. If the periods of each one stay so, the difference of phase will increase. Eventually B will be 180° in advance (or B 180° in retard).
When two waves have the same periodicity, that is same frequency, and travel at the same speed, if they travel the same distance they will keep the same phase difference.
Path difference
Path difference is the difference between the actual lengths traveled by the two waves in space.
Suppose you send two light waves from two different points.
Suppose you send wave A horizontally on the x-axis and suppose you send wave B not perfectly horizontally but with some angle from some point on the Y.axis. These two waves will meet at some point on the X-axis.
But the distance travelled by the wave A will be less than that by Wave B.
This difference in the actual path they took is path difference.
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