I think the perfect way to differentiate between genus and species is to think of both as though they represent the scientific surname and first name given to all organisms. When you check the order of classification of all organisms into different levels, genus and species are the last two levels of the classification, with "kingdom" being the first level.
Genus comes below the family level and above the species level. A genus consists of organisms with certain similar attributes or morphology. So many species are grouped under the genus level. However, animals of different species that are grouped under the genus level can't interbreed.
Species, on the other, is the last level in this classification and consists of organisms that are very identical in most ways. Organisms of the same species that are in this category can interbreed to produce fertile offsprings. While a genus consists of a group of species, a species consists of a group of subspecies.