All organisms share a common ancester: humans share a common ancestor with E. coli; E. coli share a common ancestor with an oak tree; humans share a common ancestor with an oak tree.
If I hypothesized the two organisms shared a recent common ancestor, they I would predict that their genomes would be highly similar. For example, their genomes would contain about the same number of bases, and the base sequences (especially of protein-coding genes) would be highly identical.
