hello yuliya 13 and welcome to just answer
A. The tax advantages to the business is that you will not incurr the 7.65% of social security and medicare taxes. You will also save on Futa and Suta (federal and state unemployment) and tax training taxes.
B. Advantages to the self employed person is that expenses that might be incurred in the contract position are much easier to write off on a Schedule C, and is not subject to the 2% limitation that unreimbursed employee expenses are on a Schedule A. As a self employed individual some of your mileage may be written off and if you use home office equipment, you can depreciate the equipment, thus lowering your tax liablity. If you do most of your work at home, you might even be able to claim a home office deduction. Meals or even coffee that you might buy for a client or potential client may be able to be written off at a 50% deduction.
The disadvantages of a self employed person is the increase in self employment taxes that must be paid. As a self employed individual you are responsible for 15.3% of socail security and medicare taxes, which is your share and employers share of the taxes.