In a molecular or complete reaction, all substances are shown in neutral (molecular) form.
In an ionic reaction, the substances that all always dissociate (strong) are broken into their ions.
Because lead (II) nitrate, sodium chloride and sodium nitrate all all soluble salt (strong electrolytes), they will all completely dissociate in water. They will not exist as molecules, but as ions. Remember you can't lose any mass in a reaction! The Law of Conservation of Matter still applies!
Notice that sodium and nitrate are EXACTLY the same on the reactant and product sides? They are spectator ions. Spectator ions do not change in a reaction. When you cancel the spectator ions, you're left with the net ionic reaction.
This shows us what is really changing in a reaction- the driving force for the reaction to proceed.
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