The conditions could be very different between the two bodies, and the life very different as well. At an early time after formation the minor body was more earth-like, similar to the case of our own Mars. The two bodies exchange material so life started on both. But as the moon changed, the early life evolved to cope with very different conditions. After starting with the same abiogenesis stock, life on the two bodies went their separate ways long before photosynthesis and endosymbiosis occurred on the Earth-like body, and cells took different routes on (warmed)Mars-like moon as it lost its surface water and atmosphere.
I imagine that 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 swap out functional parts, including various tamed procaryotes (like mitochondria) 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 to form the ecosystem.
So the “conventional” aliens from the major body find, upon arriving on their moon, that the rocks are alive, and quickly find ways to eat them.
