Cross-cutting is a broader term.

In parralel action, the things intercut are actions - something is
happening in each setting - and these actions are connected to each others
as actions - they have some commonality in form, purpose, or narrative
convergence: chase scenes across different eras in Intolerance. The
intercutting between two people preparing for a date (in a billion student

Cross cutting could include something that is not action, say if we cut
between shots of The Governator beating a thug to a pulp and
Peter-Huttonish landscape vistas - and (same example will do) also combine
things that are in no way parallel.

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