They are certainly related. I think originally the
type with pyre was intended for the
Herakles Acheloios scene, recalling
his Apotheosis on a pyre, all under the power of
Zeus, represented by the
eagle (see the last line of the play- "all this is not but
Zeus!). We know the people of Tarsos burned an effigy of
Herakles on a pyre every year in
his honor (as the city's founder), and Acheloios plays an essential role in the
apotheosis per Sophocles' account (in The Women of Trachis).
The
type with figure on beast (no pyre) probably indicated
Sandan, whose predecessors (Teshub, etc.) were often depicted with wings and standing on a
lion or
bull.
So, my guess is that after the initial series things got understandably confusing, especially since
Herakles and
Sandan were conflated, hence the various creatures beneath the figure on both
types.
Alternatively, there are a lot of instances of monsters or the
centaur Chiron in Sophocles' account, so perhaps the pyre-type variations are in
part due to that.
Centaur is from the Greek Kentaur, meaning (IMO) like-bull.
