der Plan
plan
An intention or a detailed idea of how you want to do or achieve something in the future.
Hast du schon einen Plan für das Wochenende?
Do you already have a plan for the weekend?

plan
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plan
An intention or a detailed idea of how you want to do or achieve something in the future.
Hast du schon einen Plan für das Wochenende?
Do you already have a plan for the weekend?

You can recognize the meaning of 'Plan' (plan/map) from the context. If people are talking about intentions, time, or goals, it means an idea or plan. If it involves a building, a city, or transportation, it means a drawing or map.
Mein Plan ist es, nächstes Jahr Spanisch zu lernen.
My plan is to learn Spanish next year.
When 'Plan' (plan) describes an intention, it is often combined with the verbs 'haben' (to have), 'machen' (to make), or 'verfolgen' (to pursue). A poetic expression is 'Pläne schmieden' (to make/forge plans).
Wir müssen für das Projekt einen genauen Plan machen.
We need to make a precise plan for the project.
In the meaning of 'Zeichnung' (drawing) or 'Übersicht' (overview), 'Plan' (map/plan) is often the second part of compound nouns. Well-known examples are 'der Stadtplan' (city map), 'der Fahrplan' (timetable), and 'der Bauplan' (building plan).
Kannst du mir auf dem Stadtplan zeigen, wo wir sind?
Can you show me on the city map where we are?
The idiom 'nach Plan laufen' (to go according to plan) is a fixed structure. It means that something works as expected or without problems. The preposition 'nach' (according to) is crucial here.
Die Vorbereitungen für die Feier laufen genau nach Plan.
The preparations for the celebration are going exactly according to plan.
idea
'die Idee' and 'der Plan' can both have to do with something you want to do. 'Idee' is often the first thought or the basic concept. 'Plan' is more concrete: you already have a better idea of how, when, or with which steps you want to do something. Learners may confuse the words because a good idea can later become a plan. As a guide: first you have an idea, then you turn it into a plan.

Für den Umzug am Wochenende gibt es schon einen genauen Plan.
There is already a detailed plan for the move this weekend.
Wir haben die Idee, im Kurs ein kleines Regal zu bauen.
We have the idea of building a small shelf in the course.