Bouldering chalk vs. sport climbing chalk: is there an actual difference?
Not in the base formula. Both are magnesium carbonate, and there's no separate chemical compound used for one discipline versus the other. Where real differences show up is in texture, format, and how each fits the way that type of climbing actually plays out.
Why bouldering leans toward certain formats
Bouldering problems tend to be short, without a chance to chalk up again once you leave the ground. That makes coverage upfront more important, and a lot of boulderers prefer loose chalk they can apply generously right before starting, since there's no reapplying mid-problem the way there often is on a longer route.
Why sport and rope climbing lean differently
Longer routes give you more natural opportunities to chalk up at rests or clip stances, so reapplying throughout is more built into the rhythm of the climb. Chalk balls are common in this context too, partly because a lot of rope-focused gyms restrict loose chalk to manage dust in a shared space with rope walls running alongside bouldering areas.

Session (150g)
Session is an 80/20 blend, built to outlast. Fine powder coats your hands on the first dip, so the grip is there immediately. The chunky ...
So the "difference" is really about habits, not chemistry
Marketing sometimes implies bouldering and sport chalk are formulated differently, but the underlying compound is the same across both. What actually shifts is texture preference, format, and reapplication habits, all shaped by how each discipline is climbed rather than by a different mix in the bag.
Does that mean one chalk works for everything?
Generally, yes. A well-balanced loose chalk works for both bouldering and rope climbing, since the formula itself isn't discipline-specific. The main consideration is format, whether your gym or crag allows loose chalk, a chalk ball, or both, rather than picking a fundamentally different chalk for one type of climbing versus another.
The takeaway
There's no separate formula for bouldering versus sport climbing chalk, just different habits and formats shaped by how each type of climbing is actually done. The same well-formulated chalk can reasonably cover both.