public companies with traded and non-traded shares

Hey,

just read that calculating Equity Value via Share Price x Fully Diluted Shares Outstanding could lead to understating Equity Value. As a reason it was stated that public companies can have multiple classes of shares, with one or more of these classes being non-traded. And therefore among these non-traded shares could e.g. have a higher percentage of shares with better dividend payout.

Can s/o approve or contradict the statement? Actually I have never heard of a listed company issuing non-traded shares, so maybe s/o can give an example.