Clover= large and shamrock = small is not botanically valid since they are the same thing- just a difference in language. Shamrock is a clover is a clover is a clover, to paraphrase. There are over 300 species of clovers in a fair range of sizes.
In the foothills from near the Canadian border to California occurs one with 3-9 leaflets on each leaf rather than the usual 3 in most species of Trifolium. Needless to say, you have a good chance of finding a "4-leaf clover" with this species, Trifolium macrocephalum, which also has a large flower head, up to 5 inches long. As well, this one is nice as a cooked green.