The true Iris variegata, or Hungarian iris, is named for the variegated patterns on the flowers. However, variegated-leaf cultivars of other species exist (e.g., Iris pallida ‘Variegata’. Tempering one’s expectations is warranted when purchasing an “iris variegata” from a nursery due to confusion, in particular if one is buying rhizomes.
Iris variegata is native to central and southeast Europe. Along with Iris pallida, it is considered one of the parent species of Iris × germanica, which itself is thought to be the progenitor of the wide variety of tall bearded irises in cultivation. There is conflicting information on this, notably the claim on Wikipedia that Iris × germanica is sterile, implying that the tall bearded irises have some other hybrid origin. Perhaps an iridophile can clarify in the comments.
Plants of the World Online from Kew has an excellent factsheet on Iris variegata (which notes “many hybrids and cultivars derived from [Iris variegata] are widely grown as ornamentals”).