The country/western two-step, often called the "Texas two-step"or simply the "two-step," is a country/western dance usually danced to country music in common time. "Traditional [Texas] two-step developed, my theory goes, because it is suited to fiddle and guitar music played two-four time with a firm beat [found in country music]. One-two, one-two, slide-shuffle." The two-step is related to the polka, the Texas waltz, and the jitterbug.
The Texas two-step is the same step known to ballroom dancers as the international fox-trot. Except for the one-step, which is just that, most Texas dances are variations of a two-step, also called a half-step, which is simply a step-close-step. The Texas two-step is generally done with two long steps and a step-close-step to two-four time. Speeded up, it's a shuffle or double shuffle, but still a two-step.
As with other country/western dances, there are many different versions of two step across the United States, and there may be no one truly "correct" way to perform a particular dance. Even individual dance halls may have their own unique variations which they consider correct.