The type species, Edaphosaurus pogonias, had sail up to the back of the skull whereas our friend last week, Dimetrodon, has a sail free portion of its neck before the skull began. As stated, the two animals had different ancestry, and this accounts fo the majority of the differences in the body, especially the sails. As with any prehistoric animal different interpretations of the skeletal material are available to us thanks to a number of different illustrators and different paleontological accounts. One such alternate interpretation is the version of M. Shiraishi which possesses a strongly iguana-like presence in the facial construction of Edaphosaurus:
The bones of the skull are strongly iguana-like, however, most of the illustrations of Edaphosaurus are not as reptilian as the above version. The skull head on actually looks much more menacing than other herbivorous skulls:
Completely incorrect, as we know them today, interpretations freely flow about the internet as well. These include illustrations and paintings of the animals as slow swamp dwelling animals requiring the heat of the sun as well as other depictions which rely heavily on reptilian influences.
One of the worst examples of reptilian-ness in Edaphosaurus representations is found in the Museum of Western Bohemia in Plezn in the western side of the Czech Republic. While the display is large and rather interesting on original inspection it contains and Edaphosaurus which is clearly using its tongue to scent the air as a typical lizard or snake does: