There are several species of equality: \begin{align} = & \quad \text{exactly equal} \notag \\ \propto & \quad \text{equality except perhaps for a factor with dimension} \notag\\ \sim & \quad \text{equality except perhaps for a factor without dimensions} \notag \\ \approx & \quad \text{equality except perhaps for a factor close to 1} \end{align}

Source: page 6 in Street Fighting Mathematics by Mahajan