When learning to dance, your awareness of different styles may be quite limited and of little consequence. In North America, particularly in the USA and in Canada, where I live, two styles are common. One is called North American (or simply American) and the other is called International. Each has subgroups. American includes Smooth (waltz, foxtrot, tango and viennese waltz) and Rhythm (rumba, cha cha, bolero, mambo and east coast swing) while International includes Standard (waltz, foxtrot, tango, quickstep and viennese waltz) and Latin (rumba, cha cha, jive, samba and paso doble). As a beginner you may neither know nor care which style is learned but eventually you will see the other style, the one you haven’t learned, being danced and perhaps wonder if you have learned incorrectly. Don’t let this shake your confidence but get your instructor to help you understand.
There are a number of organizations that publish syllabi for each style of dance. There are several recognized syllabi for the American style. Some studios, the chain studios in particular, may teach slightly different stylistic variations. The International style is governed by fewer and much more strict syllabi than American which makes it quite consistent world wide. These documents encourage a degree of standardization for footwork and technique regardless of the studio or instructor.
To an onlooker American and International dances, even those with the same name, will often appear to be quite different as indeed they are. Differences in some dances are more obvious than in others. However, it is only in competition where these differences are of major importance. Either style may be danced together in social settings. In competition each style is danced separately but the American style is not danced competitively in many countries outside of North America. There are also many dance steps that are outside the fundamental American and International curriculum. Many of these are danced both socially and competitively.