As a biologist I'm aware that few characteristics evolve more than once. We can uncover the relationships of “unrelated” species by looking at their DNA or more simply, by finding homologous anatomical features that have been inherited from a common ancestor.
The world of plants, my area of study, is so rife with morphological similarities I wonder sometimes if there are any real differences among its species. For example I see patterns of fern-like growth (circinate vernation) in emerging shoots and flowers of many unrelated species, plants that evolved long after their fern ancestors.
And we humans share so much in common with the rest of the living world that our common ancestry with plants, insects, and even fungi and bacteria, is a moot point. Even though we are only distantly related to say, sharks, we share an inherited vertebrate body plan, not to mention cellular, metabolic, and molecular features in common.