The impact of Next-to-Leading Order (NLO) QCD corrections to the differential distributions of $J/\psi$ and $\Upsilon$ mesons produced inclusively in $\gamma\gamma$ collisions is discussed for the kinematical conditions of LEP II for DELPHI and at the future Circular Electron-Positron Collider (CEPC). We take into account all sizeable contributions at LO in $v^2$ in NRQCD factorisation: 1) pure QED process $\gamma + \gamma \rightarrow J/\psi({}^3S^{[1]}_1) + \gamma$ up to $\alpha^3\alpha_s$, 2) single-resolved-photon contributions up to $\alpha_s^4$, 3) $\gamma+\gamma\to J/\psi + c\bar{c}$ up to $\alpha^2\alpha_s$ and 4) $\gamma+\gamma\to J/\psi + ggg$ up to $\alpha^2\alpha_s^3$. We will also discuss the pure QED process as a contribution to the exclusive production in ultra-peripheral heavy-ion collisions (UPC) at the LHC.