There are many different ideas of the meaning "Ballroom Dancing". The only commonality seems to be that it is "partnership dancing". There are some that assume that any dancing in a large room (ballroom) is Ballroom Dancing. Others seem to think that "Big Band" is Ballroom Dancing". A lot of these expectations are based on the experiences of the individual and seems to be generational.
The original definition (way before any of our times) was partnership dancing in a ballroom. The Ballroom dances were just the traveling dances: Foxtrot, Waltz, etc. These were the only dances at the time. The Latin dances came later (Rumba, Cha Cha, Jive, Swing, Samba, Bolero, etc.).
Even today at the professional levels, there are dual meanings being used for "Ballroom Dancing". If you listened to the center judge (Len) on Dancing with the Stars, he made comments like: You're forte is Ballroom dancing not Latin dancing. Others on the show said this is a "Ballroom Dance Competition". This reference implies that Ballroom Dancing is both styles of dancing. The "American Ballroom Challenge" televised on PBS, included both styles of dancing.
To complicate things even further, there are two different types of Ballroom Dancing. American Style and International Style. Dancing with the Stars was International Style while the American Ballroom Challenge had both American and International styles. The Foxtrot, Waltz, etc. (traveling dances) are called Standard Dances in International Style and Smooth Dances in American Style. The Rumba, Cha Cha, etc. (Cuban motion dances) are called Latin Dances in International Style and Rhythm Dances in American Style.
The International and American Styles are standardized. They are standardized for competion purposes. You need to be able to compare apples to apples and oranges to oranges. Standardization also includes the music. The music is strict tempo (does not change in speed) and is played at a specific speed for each dance.
When I first started dancing, my wife and I would scour the papers looking for ballroom dances. Most of the time we were disappointed because they weren't the ballroom dances we were expecting. They would be a band playing anything they wanted. If you asked them to play a Rumba, Cha Cha or almost anything else, they had no idea. They might be able to play it if you knew the title, but they had no idea what the specific dances were. From my experience, most dance bands are for "free style dancing". In my almost 20 years of dancing, I have found only "ONE" dance band that was actually a Ballroom Dance band. The leader of the band was a ballroom dancer.
Most ballroom dancers prefer recorded music. Dancers want to dance. A live band plays 8 or 9 songs an hour and they are 5 to 8 minutes long. That's 16 songs in a two hour dance. In the dances we run, the songs average 3 minutes in length with 10 seconds in between. We play 40+ songs in a two hour dance depending on requests. We also have around 1,000 strict tempo danceable songs available to play.
The term "Ballroom Dance" is used very loosely in the non-ballroom community. If you are going to attend a ballroom dance for the first time, it would be wise to call them first to see if you can find out their definition of a ballroom dance. Unless the dance is put on by a ballroom dance group (studio, club, etc.) there probably will not be a line of dance for the traveling dances. It has been my experience that if there is live music, it probably won't be the ballroom dancing you are used to.
In my opinion, in the United States, the most common usage for those that have any knowledge of ballroom dancing is that Ballroom refers to both traveling and Cuban motion types of dancing.