Here's what I remember from working Public Health (keep in mind this is from Canada).
Positive TB skin test (aka Mantoux test or Tuberculin test) means you have been exposed to TB, that's all. If you have a previous negative, the exposure probably happened sometime in the time frame between the tests.
The next step is to ascertain if you are symptomatic (weight loss, productive, persistent cough, hemoptysis, night sweats...). If productive cough, then you would send the sputums samples off for culture. Usually chest x-rays are done as well (even if you aren't symptomatic).
For the most part, to be infectious, you are more than likely sick...not at all up to work. The most infectious type of patient is "smear positive", they are usually hospitalized and treated until the sputum comes back negative. That's when contact F/U is inititated.
It is possible for a person with a positive mantoux and suspicious chest x-ray to be non-infectious. Each TB specialist is different, but most put people on the 6 month INH protocol to be safe. But some docs won't if they at all sense you will not be compliant (resistent strains are getting common).
Hope that makes sense!