The distinction between Level I and Level II stock trading screens primarily lies in the extent of information that is available through the Level II screen. Specifically, Level II trading quotes offer a comprehensive view that includes detailed data about current order books and the depth of the market. This means that traders using Level II can access not only the current bid and ask prices but also the various buy and sell orders that are queued in the market, providing a clearer picture of market activity. 

In contrast, Level I quotes are more limited in scope, as they focus solely on the bid and ask prices without delving into the underlying order flow. This fundamental difference makes Level II screens particularly valuable for traders who require more in-depth analysis and insights into market dynamics.