My understanding says organo-metallic = organic + metallic compunds.
One already known to me is Grignard Reagent ($\ce{RMgX}$).
But would you consider $\ce{NaOMe}$ or $\ce{NaCCH}$ as an organometallic compound? Would you consider $\ce{LiOAc}$, $\ce{LiOMe}$, $\ce{LiN(Me)2}$ or $\ce{LiMe}$?