508. Special rules with respect to section 501 (c)(3) organizations (a) New organizations must notify Secretary that they are applying for recognition of section 501 (c)(3) status Except as provided in subsection (c), an organization organized after October 9, 1969, shall not be treated as an organization described in section 501 (c)(3)— (1) unless it has given notice to the Secretary in such manner as the Secretary may by regulations prescribe, that it is applying for recognition of such status, or (2) for any period before the giving of such notice, if such notice is given after the time prescribed by the Secretary by regulations for giving notice under this subsection.
Note that 501 (c)(3) deals only with corporations and charitable organizations. These corporations and charitable organizations must give notice that they are applying for tax exempt status. If they do not, they will be presumed to be a private taxable foundation.
(b) Presumption that organizations are private foundations Except as provided in subsection (c), any organization (including an organization in existence on October 9, 1969) which is described in section 501 (c)(3) and which does not notify the Secretary, at such time and in such manner as the Secretary may by regulations prescribe, that it is not a private foundation shall be presumed to be a private foundation.
In short the incorporated church and any charitable organization must apply for tax exempt status.
There is an exception in the above code found in subsection (c). Let's see what it has to say:
When a church incorporates it is no longer a church in the eyes of the state. It instead has become a religious corporation and must follow the laws and rules that apply to corporations. When a church chooses to incorporate, it chooses freely to give up it's first amendment rights and consents to be ruled by the state through the laws of incorporation.
Where in the Code you have set out does it say the IRS differentiates between incorporated and unincorporated churches? There is no difference. The IRS looks at the organization called "church" without distinguishing corporation from unincorporation. Look at form 1023 the Application for 501 (c)(3) recognition.