A person can have a latent TB infection (LTBI) and be totally without symptoms. Here the TB is hibernating somewhere in the body, dormant. It may remain this way for decades, or longer.
LTBI is easiest to cure. A dose of INH every day for 9 months generally eradicates the TB bacillus from 96% of people with it. If you wait until TB disease occurs (with signs/symptoms like cough, night sweats, weight loss, lung lesions on chest x-ray, etc), then a 5 drug regimen is usually required, and cure rates are lower.
Granted, LTBI doesn’t often turn into TB disease if you’re otherwise healthy. But it does so often enough that treatment is still recommended. And if a person has HIV or other underlying immunocompromising diseases, then the rate of LTBI developing into TB disease is alarmingly high.
When my patients have a positive TB skin test (TST), I recommend getting a Quantiferon Gold blood test on them. Only if that’s positive do I initiate treatment. If the Quantiferon is negative, I assume the TST was a false positive (which happens very frequently).
I should add that TB is not transmitted very easily through casual contact. Usually one needs to spend a LOT of time with someone who has active TB disease in order to pick it up.