Each critter in fact carry's a wide range of genetic info;
Some hybrids (both plant and animal) carry twice the genetic material (both species) so occationally have births without a father by having eggs form that have the complete set of chromosome parts for one of the original species (the baby is not a hybrid like the mother is so is not even the same species). A type of lizzard has "virgin" births by normally having 4 copies of each of that species's chromosomes and then the eggs have pieces of the halfs of these four which form into different chromosomes with a random mixture of genes. The egg cell just completes the halves to form four new unique copies of each chromasome.
The long-distance exchange of genetic material is still quite possible as I think my previous post details and also that exchange of genetic material does not need to happen as often as cloning to still provide genetic variety.
Back to my alien creatures, I planned to have all the creatures on the planet to have the same set of genetic material (but with variations) and each creature is just modeled after the parrent but the cells could form into any creature on the planet if missing cues to form parts of a particular species. I have this story element so one creature of one species can leave the planet, the entire life of the planet can become extinct, and then the creature that left can return and quickly repopulate the world with the full set of life forms that existed before (the genetics are carried but not active for every species)