The conditions could be very different between the two bodies, and the life very different as well. At an early time after formation it was more earthlike, like Mars. The two bodies exchange material so life started on both. But as the moon changed, the early life evolved to cope with cery different conditions. They split long before photosynthesis and endosymbiosis occured onmthe Earth-like body, and cells took different routes on (warmed)mars-like moon.
Instead of green leaves, beds of black goo filling maria that harvests energy chemically from harsh radiation, in the top layers of cell-less protoplasm that turns over to, circulate the activated chemicals to the "living" parts below.
More complex life include algae (giant cells) and a massive level, of endosymbiosis instead of just eucaryotes. Semi-autonomous organelles share an enclosed bag and can swapmout functional parts, including various tamed procaryotes (like mitochondrea) that have found different tricks for processing different minerals and other resources. Feeding off the goo above, these thread through the rock of the crust mining materials and water formthe ecosystem.
They find upon arriving that the rocks are alive, and quickly find ways to eat them.