Plausible definition Consider a phase transition from phase 1 to phase 2. The order parameter is zero in one of the phases 1 or 2 and nonzero in the other.

For example, in normal (phase 1) to superfluid (phase 2) transition, the order parameter is zero in the normal phase and nonzero in the disordered phase. So in this case, the above definition works good.

However, in case of gas (phase 1) to liquid (phase 2) transition, the order parameter is taken to be $\mathcal{O}=\rho_{liq}-\rho_{gas}$. But but $\mathcal{O}$ is nonzero in both the phases 1 and 2, and only vanishes above the critical temperature $T_c$. So in this case the above definition doesn't hold good.

Does it mean that the definition

Consider a phase transition from phase 1 to phase 2. The order parameter is zero in one of the phase 1 or 2 and nonzero in the other.

is wrong?