when are organisms considered to belong to the same species
When any two individuals of the appropriate sexes or mating types can produce fertile offspring, typically by sexual reproduction. Some other ways of defining them include their karyotype, DNA sequence, morphology etc.
Species
 A species is often defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring, typically by sexual reproduction. Other ways of defining species include their karyotype, DNA sequence, morphology, behaviour or ecological niche. In addition, paleontologists use the concept of the chronospecies since fossil reproduction cannot be examined.

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Species [SEP] Introduction
All species (except viruses) are given a two-part name, a "binomial". The first part of a binomial is the genus to which the species belongs. The second part is called the specific name or the specific epithet (in botanical nomenclature, also sometimes in zoological nomenclature). For example, "Boa constrictor" is one of four species of the genus "Boa", with "constrictor" being the species' epithet.