Nest box is what they lay their eggs in so the same thing as the box you are talking about.
You'd be better off getting your info from http://www.backyardchickens.com/atype/1/Learning_Center
than from most feed store employees.
They may or may not have any experience with chickens. They do know where in the store poultry feed is stored and what other products they carry but I wouldn't call any of them I've encountered 'chicken experts'.
In spring and summer, lay usually commences at about 20-24 weeks but could be as early as 16, depending on breed. This time of year and mid winter it could take much longer because the main impetus to ovulation is daylength and more accurately, increasing day length. That is a sign of spring, warmer weather coming and a wealth of forage for new chicks. That's kind of the same with all animals.
Chickens have evolved from jungle fowl that laid a small clutch once or twice a year to the birds we have today that have been bred to lay all year.