Some researchers study hybridized phonon-magnon modes. In the strong coupling regime, when the anticrossing of acoustic and FMR dispersions is observed, the lower branch (which starts as acoustic mode and continues as FMR mode) is often referred to as the acoustic branch. The second branch starts as FMR and continues as acoustic mode is referred differently, perhaps in as an optical mode in some notations. Does it make sense?
In case of two coupled FM layers magnetized in-plane: For positive (FM-like) coupling, optical mode has higher resonant frequency, for negative (AFM-like) coupling, it is acoustic one which is higher in frequency.
An acoustic magnon is the in-phase precession of the magnetization, while the optical magnon is the out-of-phase precession of the magnetization. In FMR you have k approx 0, that means you have the collective precession of spins in the material, for FMR you have an acoustic mode. You can probe optical modes, depending on the material,with Raman/Brillouin light scattering and with neutron scattering.