You are right. shared_ptr<const T> p; is similar to const T * p; (or, equivalently, T const * p;), that is, the pointed object is const whereas const shared_ptr<T> p; is similar to T* const p; which means that p is const. In summary:
shared_ptr<T> p; ---> T * p; : nothing is const
const shared_ptr<T> p; ---> T * const p; : p is const
shared_ptr<const T> p; ---> const T * p; <=> T const * p; : *p is const
const shared_ptr<const T> p; ---> const T * const p; <=> T const * const p; : p and *p are const.
The same holds for weak_ptr and unique_ptr.