Sequence dances aren't done except at places that cater to sequence dancers. There aren't many of those and its not likely that you found one at random. A sequence dance usually consists of a 16 bar sequence repeated until the end of the song. When this is done socially, it is usually at a very low skill level, but there are exceptions. They do have competitions which are at a much higher level. Since you mentioned foxtrot and tango (although that doesn't eliminate sequence dancing), it is likely you were at a place where they were doing social level ballroom.
There are many types of sequence dances, many of which would not be recognized by a ballroom dancer, such as Blues, Four Step, Gavotte, Glide, Mazurka, Party, Quadrille, Saunter, Stroll, Sway, etc. Some may recognize some of these as predecessors to some of the more modern dances. Sequence dancing also has the dances familiar to ballroom dancers, waltz, foxtrot, tango, jive, rumba, quickstep, etc.
There are lots of other forms of dance that aren't ballroom, as you will find out when you start digging. However you can't go wrong by starting with ballroom.