There were two distinct variations on the theme and they seem to have been aimed at two distinct markets. The first variation was the so-called 'Air-King' Explorer . The second variation on the theme are 'dress Explorers.' These were standard Oyster Perpetuals in steel or gold with white (or more rarely, black) non - Explorer dials featuring markers and hands, but signed 'Explorer' on the dials. Seen in both date and non-date forms, these watches all seem to have been sold in the North American market. The Explorer Date bears a model number 5700, previously unseen on any other Explorer (the non-date model is a model 5501, 5504, which interestingly is more often seen on Explorers with the standard dial).
It seems that these watches were made in the 1950's or 1960's, when Rolex was unsure of the Explorer's success, and attempted to increase the popularity of the watch by broadening the line. When the mainstream Explorer began to sell, these 'piggyback' models were withdrawn. As a result of its limited production, these models are becoming extremely rare and are presently sought after by collectors.