$x^3 \equiv x(mod$ $3)$ for all x, whereas obviously $x^3$ and $x$ are not algebraically congruent $(mod$ $3)$. What does it mean to be algebraically congruent?. In this case the two polynomials can be viewed as $x^3+0x^2+0x+0 \equiv 0x^3+0x^2+x+0$, so for example the coefficients for $x^3$ are 1 and 0 which are not congruent $(mod$ $3)$. Is that right?