Old-time tunes vary greatly in rhythm and style depending on the purpose of the jam, the region the band is from, and the type of dance typical to that region. See this example of two stepping to understand how the music and dance works together
Breakdown: A breakdown can mean a wide array of up-beat old time tunes used for many dance styles. It may have a heavier beat than a reel but the term is used pretty interchangeably with the term reel. Breakdowns are played in 2/4 and 4/4 time. Example Follow this link to read a forum on breakdown style
Reel: A reel is a Scottish dance tune that spread to the British Isles and North America. It is played in 2/2 or 4/4 time.
Waltz: A waltz is a traditional German folk dance that is played in 3 /4 time
Jig: A jig is a traditional Irish dancing tune that is not played often in American Old Time music but can sometimes accompany clogging. It is played in in 6/8 time
Schottische: A schottische is a bohemian dance tune that spread to Europe and the United States. It is traditionally played as a slow polka but is usually played in 4/4 time breakdown style in Old Time.
Here are examples of how playing tunes in different styles alters how it sounds: Slow polka / Breakdown