It is consistent that all ultrafilters are the same in the following sense: for any free ultrafilters $\mathcal U,\mathcal V$ on $\omega$ there exists a finite-to-one map $f:\omega\to\omega$ such that $f(\mathcal U)=f(\mathcal V)$. The latter statement is called NCF, the Near Coherence of Filters. In some situation it is very helpful principle. It has been thoroughly studied by Andreas Blass, see his papers: I, II, III.

It is consistent that all ultrafilters are the same in the following sense: for any free ultrafilters $\mathcal U,\mathcal V$ on $\omega$ there exists a finite-to-one map $f:\omega\to\omega$ such that $f(\mathcal U)=f(\mathcal V)$. The latter statement is called NCF, the Near Coherence of Filters. In some situation it is very helpful principle. It has been thoroughly studied by Andreas Blass, see his papers: I, II, III.