Time is the answer to many things and that's true for chronic vs acute telogen effluvium. It's not true to say that chronic telogen effluvium is simply acute telogen effluvium that goes on for a longer time (despite the widely held myth) but it's a good starting point to understand the differences.
Patents with acute telogen effluvium (ATE) experience sudden onset of shedding, often 2-3 months after a trigger, such as low iron, crash diet, medication, severe stress, or thyroid problem. Once the trigger is corrected, the shedding resolves in 6-9 months. Treatment is focused on fixing the trigger. In true ATE, the density returns back to normal after about 9-12 months and sometimes sooner.
With chronic telogen effluvium, the shedding starts suddenly as well, but often blood tests are normal and the shedding goes on for many many months to many many years. Because there is no easily identifiable trigger, treatment can be more challenging. In CTE, the density does not return to normal but may in some cases once shedding slows.