What you're talking about is the corporate veil. It's a legal concept that separates the shareholder from a corporation or the member from the LLC as far as liability goes.
With an LLC, you as a member (owner or part owner) can take a distribution. Pretty much anything goes as long as there's still enough left over for the company to operate and fulfill its obligations. Obviously this is ill defined, but it's really there just to stop you from doing something like taking out a loan on a new LLC, taking all of cash from the loan as a distribution, and then declaring the entity insolvent with no attempt to repay. If you pull some kind of fraud like that, this will pierce the corporate veil and creditors can then seek your personal assets as compensation (other procedural violations can cause this piercing as well). That said, if you dot your i's and cross your t's, there's nothing they can do in a bankruptcy but try to extract what the entity is liable for from the business' inventory and non-inventory assets.
Corporations work slightly differently. Unlike an LLC were the member can't take a salary, shareholders can be salaried employees of the entity and legally collect money from the company that way. They can also collect dividends. Other than those things and selling shares, I don't believe there's any other way to take money out of a corporation as a shareholder. Violate those rules, the veil is pierced, and they can legally go after your personal assets.