Mind map is not really equivalent unless you restrict connections to rigid hierarchy, but ability to make more flexible connections is part of why you'd choose mind map software over an outliner.

FWIW, orgmode does export outlines to Freemind mindmapper (using ox-freemind.el which is part of the org-plus-contrib packaging at Emacs' elpa repository.

As some others have said, orgmode does get beyond hierarchical structure of outlines by allowing searches on tags, properties, dates, and other items, which then consolidates all relevant headings -- potentially from dozens or hundreds of different files -- in the Orgmode "Agenda". They are thus visually connected in the Agenda, which in addition to consolidating in one spot provides easy access for directly editing, jumping between the relevant headings, and more.

I use Orgmode, have used Freemind a little bit in the past, but find Orgmode a far more flexible tool; Orgmode has so many features that go beyond mere outlining or mind-mapping.

Freemind is primarily hierarchical but you can easily make non hierarchical links (hyper and visual). Also you can add multiple tags/attributes to nodes

Exactly. The org-mode -->> freemind conversion works fine, translating textual hierarchical outline to freemind's graphical representation. I don't think the current exporter has support for exporting non-hierarchical links (e.g., org-mode tags) to freemind, but that would be a nice feature.