There is quite a big difference between a public trust and a private trust. Both of these trusts if charitable, are formed for the benefit of the people. The public trusts however are those that are formed for the benefit of the general people allowing everyone to benefit from it. It is not limited to a particular group of people.
On the other hand, a private charitable trust is the one that is is open to provide benefits only to a small group of specific people. Another major difference between private trusts and public trusts is that public trusts have a wider domain of work whereas private trusts have a limited domain for operation.