Winston has given you a good answer.
To address your final question - "Can I save money this way?" As a sub-contractor, you will have employer and employee portion of FICA and Medicare to pay, in addition to normal federal and state income taxes. The costs of your truck, tools, etc. (all of the expenses you incur in the production of your income) will be directly subtracted from your Gross Revenue, rather than listed on Schedule A and subject to 2% of your adjust gross income.
However, as a sub-contractor, you have the option of working for more than one contractor. This gives you the option to "adjust" your pricing - depending on the quality of your work and the customers you pursue - aiming for the higher valued homes is usually the method of charging a higher hourly rate and, if your work is good enough, not only getting the higher rate, but having these customer recommend their friends and neighbors.
If you are asking about making a change in payment method to you - this depends on whether the relationship changes between you and your employer. If the relationship doesn't change, IRS will say the change in status and payment method are not permissible - either you are an employee or you are an independent contractor.
If this does not answer your question, or raises other questions, please let me know.
Public Accountant , Tax Preparer
30+ years in Public Accounting and Tax Preparation