Biology Genus vs Species??!!?

There are two components to relationship because there are two components in evolution. These two components are genealogy and morphological disparity. Traditionally, the genus is used to group species that are very similar morphologically because until recently (since the 1970s), it was not possible to determine genealogical relationships precisely. Starting in the 1970s, scientists have used molecular techniques to determine how long ago two organisms may have shared a common ancestor.

Even though humans are not classified in the same genus as the chimpanzee, we do share a more recent common ancestor with chimps than chimps do with the gorilla and orangutan. So, if we based classification on genealogy alone, then we can make a case that humans should be classifiied in the same genus with the chimp. Almost all scientists would not do that because they do realize that chimps are different enough morphologically from humans to be placed in a different genus. In fact, chimps have traditionally be placed in a different family than humans. Chimps, gorillas and orangutans have traditionally be placed in the family Pongidae, but humans are placed in the family Hominidae on the basis of morphological disparity. That arrangement is however unacceptable to a new generation of taxnomists who want to emphasize genealogy and de-emphasize, even ignore, disparity. These taxonomits instead want to lump the chimp, orang, gorilla and humans in the same family, i.e. Hominidae. The new arrangement is not satisfactory because apes are quite different from humans. Apes are quadrupeds, with small brains, and humans are bipeds with much larger brains. In fact bipedalism is so rare among mammals that this feature alone is reason enough to recognize australopithecines and humans as a different family than the quadrupedal apes.

Back to your question, are ther any species that are more closely related to another species from a different genus than it is to a member of its own genus? The answer is yes. For example, take the North American ratsnakes of the genus Elaphe, e.g. Elaphe guttata (the corn snake). It is actually more closely related to North American snakes in the genus Lampropeltis (kingsnakes), Pituophis (gopher and pine snakes), Rhinocheilus (long-nosed snake) and others than it is to the Asian and European members of the genus Elaphe, such as Elaphe climacophora, Elaphe mandarina and others, if you are only concerned with genealogy, because Elaphe guttata, Lampropetlis, Rhinocheilus, and Pituophis share a common ancestor with each other more recently than any of them do with Elaphe species from Eurasia. Yet Elaphe guttata are more similar to Eurasian species of Elaphe than it is to its North American relatives. What do scientists do in this case. Do we split up Elaphe even though the North American species are not really that different from the Eurasian speies? Or do we keep the Elaphe guttata in Elaphe even though it is genealogically closer to Lampropeltis, Pituophis and Rhinocheilus. The disagreement on how exactly to classify organisms in similar types of situations is a major source of disagreement among different schools of taxonomy.

Individuals from different genera are less closely related than individuals from the same genus. Having the same species name of the binomial does not indicate relationship. In other words, it's like having the same first name, but different last names. John Smith, and Betty Smith are more closely related than John Smith and John Jones, even though Smith and Jones have the same first name.

you could call the use of the same species designation for lifeforms from separate genuses as just a coincidence. There is no intended link that comes from the common use of the term. you should think of it as pretty much an adjective, a red dog and a red scorpion would not be related in any way, and would only have redness as a common trait. the important part is dog and scorpion, not red and red.