Int'l Latin Dance is Cha Cha, Samba, Rumba, Paso, Jive, your classic 5 dance.
Showdance, as a generic term, is often confused with Theatre Arts and Cabaret (there are distinct differences between these three division as well, but the lines have become very burred lately.) Most comps in the United States offer one of these generic divisions, where any couple can do anything to any music, smooth/standard or latin/rhythm or interpretive.
Latin American Showdance, also called South Amercian Showdance or simply Latin Segue for short, is a different competition all together. Latin Segue is a World competition where each country can send two representatives to compete is a "showdance" like setting. Each couple picks their own music and choreography. It is nicknamed "Segue" in that each couple is allowed (encouraged) for there to be more than one dance within the show, segueing from one to the next,ie rumba to cha cha to samba to paso and back to rumba.
However there are many rules about how much closed work vs open work, how many lifts and the time spent in the air, etc. It is very involved.
At Emerald they held the qualifying competition to pick our two US representative couples. Then those couples move onto the World Segue competition (which travels to different countries, recently at USBC in Miami). They will be watched by an invigilator with a stop watch to make sure they are within the many various and restrictive rules and then go through rounds of eliminations.
There is also the Ballroom Segue(smooth/standard) version of this competition which is incredibly involved and meticulous with rules.
At any competition, in the United States and Canada that has a showddance division, you will often see several couples using that as a rehersal division for their Latin or Ballroom Segue, to get ready to take it to Emerald and hopefully qualify for the following year.
Hope that helps
Larinda McRaven