Liouville’s approximation theorem (at least, in the form I've seen expressed in several sources after a quick Google search, for instance this and this) states that if $\alpha$ is an algebraic number of degree $d \geq 2$, then there is a constant $c=c(\alpha)$ such that $$\left|\alpha - \frac{p}{q}\right| > \frac{c(\alpha)}{q^d}$$
for all rational $\frac{p}{q}$. This seems to be equivalent to the claim that there are only finitely many rational $\frac{p}{q}$ obeying $$\left|\alpha - \frac{p}{q}\right| \leq \frac{1}{q^d}$$
On the other hand, Dirichlet's approximation theorem asserts that for any irrational $\alpha$, there are infinitely many rational $\frac{p}{q}$ satisfying $$\left|\alpha- \frac{p}{q}\right| \leq \frac{1}{q^2}$$
These two theorems seem to be flatly contradictory in the situation that $\alpha$ is an algebraic irrational number of degree $2$ (say, $\alpha=\sqrt{2}$). What explains this discrepancy? Or is the statement of Liouville's theorem above in fact incorrect, and we require that $d \geq 3$?