In botanical terms, all three are generally defined as a group of offspring descended from a common ancestor which share common morphological and/or physiological characteristics. In cannabis, there is an unofficial distinction.
A cannabis strain can be defined as a group of plants created asexually through clonal propagation. This is the most common form of plant production in the marijuana industry. Clones, by definition, are nearly identical genetically with the exception of the random mutations during plant cell division in the development of the “mother plant” (the plant from which a population of clones is generated). Mutations are almost always deleterious. A single mother plant creates a finite number of progeny so the maintenance of a strain requires cloning from the progeny of the original mother. Mutations accumulate with each successive generation so that, eventually, clone quality (e.g. cannabinoid profile.) deteriorates to the point that the strain is abandoned. Some may refer to this mutational load as genetic drift but this is a misnomer.
A cannabis variety (or cultivar) can be defined as a group of plants created sexually through propagation of seed. The seed of selected plants (those expressing the characteristic of interest) are used for planting the following generation. Mutations undoubtedly occur during sexual reproduction but they only impact a single individual which can be removed from the population by the breeder. As soon as an individual carrying a mutation is used as a mother plant, all derived progeny will inherit the mutation.