What is difference between breed, variant, subspecies and species?
A species is commonly defined as the largest group within which interbreeding produces viable offspring.

A sub-species is a subgroup below the level of a species.  One definition is a group which can interbreed successfully with other subspecies, but does not do so in practice (e.g. due to geographical isolation).  Other terms like variety, form, etc., may be used in some domains to indicate various groupings below the species level.

A breed usually refers to a population of a domestic animal that has been selectively bred for specific characteristics.

A population is a set of individuals within a species that live in the same geographical region.  Depending on rates of gene flow, different populations within a species may eventually differentiate into subspecies or distinct species — this is known as allopatric speciation.