Binomial nomenclature: Why am I seeing different genera with the same species name?
Two different species can have the same species epithet if they belong to different genera ('species name' is referring to the full binomial name). Consider for example Pinus glabra and Ilex glabra

P. glabra



I. glabra



Two species can be have the same genus name (meaning they belong to the same genus) and will therefore necessarily have different species epithets (otherwise we would name them exactly the same way which would be very confusing). Consider for example Pinus glabra (again) and Pinus resionosa

P.glabra



P. resinosa



As a consequence, if two species share the same species epithet then it tells you nothing about how closely related they are. If they share the same genus name, then they belong to the same genus (except exceptions probably!).

For the above examples, the term glabra comes from "glaber" (latin) which means "Hairless". So the only thing you can tell from P. glabra and I. glabra is that they are probably both hairless when you compare them with their respective closely related species.