Basically, by how long you've had it and what your treatment has been.

Acute is how you usually start out; severe pain, swelling, contraction of the scrotum/testes (via the autonomic cremaster muscle), possible swollen lymph nodes throughout the body on the affected side(s), creeping of the pain up the spermatic cords into the lower periphery of the abdomen (between pubic bone and hip), et cetera.

Then you are usually treated with antibiotics for a few weeks to a few months. This may provide some relief, but if you are destined for a chronic case, it never goes away entirely.

Then, after you're off the antibiotics, and it's been a few months, but symptoms persist (if a bit different than during the acute stage, usually not quite as bad), you're looking at a chronic case.

An acute case usually centers around an infection (although its underlying cause can actually be something else, such as lymph system congestion, chronic allergic state, physical blow to the groin, etc).

A chronic one is primarily based on the after-effects of the infection, along with the persistence of any underlying causes -- like lymph system issues and exposure to allergens, in my case.

Acute cases sometimes respond to antibiotics, although never very well (the affected tissues don't absorb anti-b's from the bloodstream very well). Chronic cases are outside the scope of the vast majority of doctors, and they become a (EXPENSIVE!) liability very quickly.

Chronic cases can take months to years to fully resolve -- and in some cases, it can become a periodic, life-long affliction (I know that's scary to hear!). The best treatments seem to be found in various herbs and supplements, along with a strong exercise/general health regimen.

Everyone's situation is a bit different. The best way to get a solid understanding of yours is to talk it out with the group here.