This is a very brief history of how dances came to be.
Folk dancing has always been around but less formal than today. Different tribes (and later countries) had different traditions. With travel and writing came a shared tradition. By the end of the sixteenth century, the Branle, Pavane and Galliarde had been recorded. Dancing became popular in royal courts - especially in France. In the latter part of the seventeenth century, the Minuet and Gavotte dominated. Steps were extremely complex and decorative. Many Old-Time dances use ballet steps and foot positions. This is because they are partly derived from court dances whose steps were formalised before ballet left the ballroom for the stage.
The Waltz is probably based on an Austrian / German folk dance - the Ländler. This had a medium tempo and the step groups or figures varied from region to region. The faster Viennese Waltz became popular at the end of the eighteenth century. The modern Slow Waltz allows time for more complex steps. The Waltz dominated Europe for the next century, despite the arrival of the Polka, Mazurka and Schottische.
Then America took over - although much of the inspiration was actually African. It contributed the Two-Step and Barn Dance at the end of the nineteenth century and the Boston, One-Step and Rag at the start of the twentieth. However, its real breakthrough was the Foxtrot in 1914. This started as a medium tempo informal dance which split into 2 distinct styles. The slower, smoother form became the modern Foxtrot. The faster, jerkier form was called the Quick-time Foxtrot and Charleston for a while before settling as the Quickstep. The uncontrolled Lindy Hop and Jitterbug led to the formalised Jive, Swing and Rock 'n' Roll styles.
The Paso Doble is Spanish and the Tango has Argentine origins. However, the modern ballroom Tango bears very little resemblance to the Argentine, having been sanitised for the British public. Other Latin American dances are the Rumba, Mambo, Cha-Cha-Cha, Samba and Bossa Nova which are largely derived from African rhythms.