Organometallic Compounds

An organometallic compound contains at least one direct metal-carbon bond.
$C_2H_5MgBr$ (Grignard reagent): the ethyl group is attached directly to Mg, so there is a Mg–C bond.
$K[Pt(C_2H_4)Cl_3]$ (Zeise's salt): ethylene is bonded to Pt through its $\pi$ electrons, so Pt–C bonding is present.
$Ni(CO)_4$ (nickel tetracarbonyl): each CO is bonded to Ni through carbon, so there are Ni–C bonds.
$Al(OC_2H_5)_3$ (aluminium ethoxide): each ethyl group is attached to oxygen, and oxygen is attached to Al. The linkage is Al–O–C, so there is no direct Al–C bond.
So aluminium ethoxide, $Al(OC_2H_5)_3$, does not have a metal-carbon bond.

In $\pi$-bonded organometallic compounds, the metal is bonded to the $\pi$ electrons of an unsaturated organic molecule. The symbol $\eta^n$ (hapticity) shows how many carbon atoms are bonded to the metal.
$K[PtCl_3(\eta^2-C_2H_4)]$ (Zeise's salt): Pt is bonded to both carbons of ethylene through its $\pi$ electrons; $\pi$-bonded.
$Fe(\eta^5-C_5H_5)_2$ (ferrocene): Fe is sandwiched between two cyclopentadienyl rings, using their $\pi$ electrons; $\pi$-bonded.
$Cr(\eta^6-C_6H_6)_2$ (dibenzene chromium): Cr is sandwiched between two benzene rings; $\pi$-bonded.
$(CH_3)_4Sn$ (tetramethyltin): each methyl group is attached to Sn by an ordinary Sn–C $\sigma$ bond; it is a $\sigma$-bonded organometallic compound.
So $(CH_3)_4Sn$ is not a $\pi$-bonded organometallic compound.