No. Critical points are where either the derivative is 0 or where the derivative does not exist. Points of inflection are where the secondderivative changes sign. That has to be where the second derivative is 0 or does not exist although not all such points are inflection points.
For example, if f(x)= x3- 3x, then df/dx= 3x2- 3 so the critical points are x= 1 while d2f/dx2= 6x. The only inflection point is at x= 0.