A post-bac includes any classes you take after you already have a degree. A lot of people (myself included) went back to college as a non-degree seeking student to take some additional courses to fulfill pre-requisites or to boost GPA. There are official post-bac programs that are offered by some universities. Those tend to be more structured and you will be given a set of classes to take, instead of picking them yourself a la carte style.
A second bachelor's will include all of the general education courses associated with getting a full degree. Also, let's say you need to finish organic chemistry courses. If you do a post-bac, you would just take ochem 1 and 2, but if you did a full chemistry major, you'd have to take additional ochem classes, pchem classes, a whole series of biochemistry, and might end up taking more classes and spending more time than you actually need.