A very important appendix to your statement, which is often overlooked in initial training, is that a wing will stall at a constant angle for a given configuration.
Extending the trailing edge flaps normally increases the CL for a given AoA but reduces the critical AoA. CLmax increases. Ie, you are shifting the CL/AoA curve up and to the left.
Extending leading edge flaps or slats normally shifts the graph up and to the right - ie little or no change in CL for a given AoA, but critical angle of attack is increased with a corresponding increase in CLmax.