What form of natural selection did Darwin and Wallace discover?

In the 19th century Darwin extensively observed animals in the Galapagos Island and synthesized a complete unifying theory that helped explain the vast diversity, the unity of life, and the ways in which organisms are suited to their environment: this theory became known as decent with modification, or in modern terms evolution.  But to understand the essence of evolution he needed to explain how evolution occurred and with notes taken on his Voyage on the Beagle, he found that organisms slowly adapted to and need to explain how adaptations arise, thus he formulated his theory of natural selection to explain how populations slowly inherited favorable traits.

Different forms of natural selection, directional, disruptive and stabilizing, are involved in altering the frequency distribution on which phenotype in a population are favored. 

Directional selection occurs when conditions favor organisms that exhibit one extreme of a phenotype range, thereby shifting the population's phenotypic character in one direction.

Disruption selection occurs when conditions start to favor organisms in a population that contain both phenotypic extremes of a phenotype distribution.

Stabalizing selection occurs when the environment in which a population inhabits favor the intermediate phenotype, thus decreasing variation to maintain the phenotypic character.

Wallace came to similar conclusions and published his work before Darwin did, but he states that Darwin's extensive work in the field gives him more credit for the discovery of evolution.