* Barriers are useful when you have a bunch of threads and you want to synchronise across of them at once, for example to do something that operates on all of their data at once.
* Latches are useful if you have a bunch of work items and you want to know when they've all been handled, and aren't necessarily interested in which thread(s) handled them.
To add to this: I don't get why C++ distinguishes a latch from a barrier. Both of them are effectively a counter with the ability to decrement that counter (in a thread safe way) and the ability to wait until the value reaches zero (or return immediately if it is already zero). The only difference is that is a latch does those things separately from different threads while a barrier does them both at once in every thread. That's even reflected in the similar method names: .count_down() and .wait() on latch, and .count_down_and_wait() on barrier. Why not make all three methods be methods of one class, which simplifies the API and potentially allows other use cases?
How could either of them be implemented with a counting semaphore? It seems like it waits in the wrong (opposite) situation than barrier and latch need, but maybe I'm just not being imaginative enough.
In short (copied from that answer):
* Barriers are useful when you have a bunch of threads and you want to synchronise across of them at once, for example to do something that operates on all of their data at once.
* Latches are useful if you have a bunch of work items and you want to know when they've all been handled, and aren't necessarily interested in which thread(s) handled them.
[1] https://stackoverflow.com/a/62631294