  In this paper, we consider the embedding relations between any two $\alpha$%
-modulation spaces. Based on an observation that the $\alpha$-modulation space
with smaller $\alpha$ can be regarded as a corresponding $\alpha$% -modulation
space with larger $\alpha$, we give a complete characterization of the Fourier
multipliers between $\alpha$-modulation spaces with different $\alpha$. Then we
establish a full version of optimal embedding relations between
$\alpha$-modulation spaces. As an application, we determine that the bounded
operators commuting with translations between $\alpha$-modulation spaces are of
convolution type.
