You have:
Ionic (eg Pb+2Cl<sup>-</sup>+2Ag<sup>+</sup> <sup>_______</sup>> Pb<sup>2+</sup> +2Cl<sup>-</sup> + 2Ag)
Net Ionic (eg Pb+2Ag<sup>+</sup> <sup>_______</sup>> Pb<sup>2+</sup>+ 2Ag)
Half Formula's (eg Pb<sup>_______</sup>> Pb<sup>2+</sup> +2e<sup>-</sup>)
Full Formula (eg 2HCl+Mg <sup>_______</sup>>MgCl<sub>2</sub>+H<sub>2</sub>)
Thats all I can think of at the moment.
Basically ionic, include all ions
net ionic, do not include spectator ions (ions that are the same on both sides)
half equation, only concerns one ion
full equation, no ions ie Mg<sup>2+</sup> +2Cl<sup>-</sup> becomes MgCl<sub>2</sub>