Here is probably more than you wanted to know, from the OED. "The "shamrock" of the legend has been conjecturally identified with many different plants, e. g. the white clover, T. repens; the red clover..., the black medic ... (leaving out sci. names), the wood sorrel..., and the water cress. The name is now most commonly applied to the lesser yellow trefoil, Trifolium minus, which is the plant most frequently worn as an emblem on St. Patrick's Day."
The wood sorrel, Oxalis, is often seen in florists and sold as shamrock- it has larger, often 4-lobed leaves. A yellow species comes from Europe but is not native to the British Isles. It is often a troublesome weed.
I think the T. minus, mentioned in the OED, could be the same as the T. dubium I mentioned earlier. Names change as more data is accumulated on species, and can be confusing unless you know quite a bit about plants.