Ballroom dancing is broken down into Fox Trot, Waltz, Quickstep, Viennese Waltz and the ever popular Tango. There are also sub categories like The Argentine Tango. Ballroom dancing tends to be slower, excepting for the Quickstep and Viennese Waltz. In ballroom you would always step forwards on a heel, keep the knees slightly relaxed and travel well at all times. The upper body is usually held in contact with your partner with a well extended back and elongated neck, to give an elegant look to your dancing. Ballroom is more difficult because of it being so slow and controlled.
Latin American dancing includes dances like Swing, Rumba, Samba and Mambo. There are many subcategories here including Cuban Rumba, Salsa, Rock 'n Roll, etc. Latin dances tend to be faster, excepting for the rumba. There is a lot of hip action, and in the Latin dances the dancer never steps on a heel. The toe always leads the way. The Latin dances are easier to master than the ballroom dances, as you are not dancing as closely with your partner.
If you go for social dancing lessons, you will generally learn a mixture of all of the above dances. If you would like to specialize in either ballroom or Latin American, the best thing to do is take yourself off to a studio that specializes in entering competitions. If you do go onto the competitive scene, be warned that the dancers practice for about six hours a day to get their movements perfect and in sync with each other. If you thought pointe shoes were killing, try dancing in high heels for a day.
All in all learning to dance is fun and rewarding, and you can do it with your partner and both have lots of laughs in the process. Of course you can do it for exercise or fun and don't have to progress to the competitive levels that some couples do.
So come on ballet dancers, put away those ballet dancing slippers for an hour a week and try something different for a change.