Employees
Employees are paid through your payroll system. You write their checks. Taxes must be taken out on all employees. An employee is given training for the work that they will be expected to do. The work that an employee does is controlled by you or others in your business. You are their boss. An employee works only for one employer. Employees are entitled to certain benefits, whether it be vacation time, health insurance, retirement benefits, etc.
Contractors
Contractors are often not on the payroll. They operate under their own business name, and often has employees of their own. Contractors have a separate business checking account, and they give invoices for work done. Contractors have their own tools, materials and equipment. They also are free to set their own hours. They do not have to report to work at a certain time. Taxes are also not withheld from a contractor's check. They will be classified on your taxes using a 1099 non employee compensation form.
It is very important that your workers are properly classified. By improperly classifying an employee as an independent contractor, you may be responsible for paying past taxes for that employee, and the wrong classification can really cause trouble if an ex-employee/contractor tries to sue for back wages, health insurance, retirement, etc.. So, moral of the story is, always make sure your employees are properly classified as such. The bottom line is that you are in control of your employees, and independent contractors pretty much control themselves.