Such as the natural linewidth is defined to be angular frequency, while the absolute frequency of laser is frequency. By far I haven't found a good way not to learn it by roting. Would anyone be willing to share with me your thoughts if you have a better way?
Frequency is frequency. You can say that a particle executing SHM in a cycle which repeats once per second has a frequency of 1 Hz. Or you can say that the displacement of the particle at time $t$ is $A\sin(2 \pi t)$, in which case you have assigned it a phase angle $\theta = 2 \pi t$ and you can say that its angular frequency in phase space is $1$ Hz. Although I think it would be more common to say that its angular velocity in phase space is $2 \pi$ radians per second.