In taxonomical sciences, we might have often seen the terms "cultivar" and "variety" being used interchangeably. Though they possess many similarities, they are quite different actually.
Both cultivar and variety can be called as types of botanical species that show considerable differences from other members of the same species, which could be anything from colour, size, adaptability, resistance, etc. But the essential difference lies in the fact that while the variety of a species usually grows wild, undisturbed in the nature; the cultivar, as the name suggests, is cultivated by humans (Cultivar = "Culti(vated) var(iety)"].
This human interference could be by producing hybrids from two or more varieties of a species or via genetic mutations. It is inevitable, then, that the cultivar has to have some genetically superior make-up (desired characteristics etc.) for humans to select, cultivate and propagate it. But that need not be the case with a variety.
When propagated via sexual reproduction, a variety being genetically uniform is more likely to produce genetically similar progeny. However, the progeny of a cultivar, which is a hybrid, could be something very different (depending upon which allele gets expressed). So to produce identical plants, a variety can be propagated through seeds; but in case of the cultivar, clones can be produced by vegetative propagation only.
In systematics, both variety and cultivar come next to the species in hierarchy, but when it comes to the naming conventions, a variety is written italicized in small case (with var. added before it).The cultivar, however, has the first letter capitalized, put inside single quotes and is never italicized (cv. is written before to represent it).