In the examples above the translation is in present continuous, but in Spanish the sentence is just using present simple. Is there a difference in meaning between:
En dos dias me mudo a Mexico.
En dos dias estoy mudandome a Mexico.
The translations you see in this lesson about this use of the present tense in Spanish, for example: "Next year I am travelling ...", "Tomorrow I'm going..." are referring to a future event. They are not using the present continuous tense in English to express an action that is happening continuously at the time of speaking. We are saying "I'm travelling..." as in "I am going to travel..."
The Spanish sentence is using the simple present, e.g. viajo, voy... because we use this tense to refer to a future event, as explained in the lesson.
I hope this helped clarify your doubt.
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