A non-exempt charitable trust must file Form 990-PF, if the trust is described in section 4947(a)(1) and is treated as a Private Foundation. These trusts will be treated as a Private Foundation if they do not meet the requirements of section 501(c)(3) public charities.
A charitable trust will be considered as a section 4947(a)(1), if the trust is not exempt from taxes under section 501(c)(a), devotes all its unexpired interests to one or more charitable purposes, and allows a charitable deduction.
W is a charitable trust but it is subjected to excise taxes and allows a charitable deduction. W is not considered as a public charity as it doesn't meet the requirements of Section 501(c)(3). W has to file Form 990-PF as it a non-exempt charitable trust that is treated as a private foundation.
The non-exempt charitable trusts that are treated as private foundations are subjected to private foundation excise taxes. Any trusts that are not subjected to an excise tax are not considered as private foundations and have to file the Form 990 or Form 990-EZ depending upon their gross receipts.