Do these two phrases differ from each other?
1. "Please watch some movies about London ONCE you plan to go to the city." 2. "Please watch some movies about London BEFORE you plan to go to the city." Do these two phrases differ from each other?

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Answer

I agree with Michael's comment about the first sentence.

As to your question, the 2 sentences have different meanings. The first one speaks about watching the movies AFTER you have made your plan. The second one speaks about watching them BEFORE you make the plan.

Answer

1. Once = immediately after
It's much more natural to say "once you have planned"