Short answer. Pole dance is the practice you meet in a weekly class: technique, flow and choreography. Pole sport is pole as a judged competition, with categories, compulsory elements and a score.
People use both phrases loosely. On a Brussels timetable, the class is almost always pole dance even when the moves are athletic.
Pole dance
Pole dance is training and performance on a vertical pole, mixed with floorwork. A class might chase clean spins, a short phrase of choreography, or strength. The point of the hour is the practice itself, or a show, not a rulebook. Heels, exotic and flow sit inside this family. They are aesthetic and technical choices, not a separate sport.
In Brussels, the studios in the directory advertise classes in this sense. Flow Factory describes its pole path as progressive technique from a first class through intermediate level 3, plus flow, heels and workshops.
Pole sport
Pole sport is the competitive version. Athletes perform a routine, often on a pole of a stated diameter, and judges score difficulty, execution and artistic components according to a code. Federations and amateur contests each write their own code. A competition category is not the same label as “level 2” on a studio website.
Training for that can look like a normal class plus extra work: repeating elements, building a routine, and filming it. It does not require you to abandon dance classes. Many competitors still take them.
This guide does not rank Brussels studios as competition schools. No public ranking is being cited. Flow Factory does say that a private class can be used to prepare a performance or a competition. That is a use of a private lesson, not a claim that the studio runs a sport team. Private lessons lists who has actually published private teaching.
What to book
Book a beginner pole class if you are starting. Book a workshop or a private if you have a routine to build. Use the word “sport” when you mean a contest. Using it as a synonym for any athletic pole class makes the timetable harder to read, which is why the two are split here.