"Oxalis Deppei", "Oxalis Regnelli", and "Trifolium Repens" are the botanical names for a few of the (many) varieties of trifoliate (three-leaved clover) "Lucky Shamrock" plants.
They are actually more native to South America than Ireland.
Four (hope, faith, love, luck) and more-leaved clovers are about a 1 in 10,000 mutation.
"Oxalis tetraphylla" is a four-leaved (wood) sorrel a.k.a. "Lucky Clover".