Angle of friction: It is the angle made by resultant of the limiting fractional force Fmax the normal reaction N with the normal reaction. In following diagram, $\beta$ is angle of friction

Angle of repose: It is defined as the minimum angle of inclination of a plane with the horizontal for which a body kept on it will just slide down on it without the application of any external force

In following diagram, $\alpha$ is angle of repose

In fig(1),we get, $\beta=\tan-1µs i6 k $

& in fig(2),we get, $\alpha=\tan-1µs $

Hence, we get $\beta=\alpha$ i.e. Angle of Friction=Angle of Repose

Though value of both is same their significance & application are different.