
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?

map / plan
A schematic drawing or map that shows the structure of something, for example a city map, a building plan, or a timetable.
Laut dem Stadtplan ist die nächste U-Bahn-Station gleich um die Ecke.
According to the city map, the nearest subway station is just around the corner.

to go according to plan
Describes that an action or event happens exactly as it was predicted or organized beforehand.
Bisher läuft bei dem Projekt alles nach Plan.
So far, everything in the project is going according to plan.
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
Idee and Plan can both refer to a possible undertaking. An Idee is initially an Einfall or an open possibility. A Plan usually shows that the undertaking has already been more firmly decided on or concretely prepared.

Für die Reise haben wir bereits einen Plan mit festen Terminen und gebuchten Unterkünften.
We already have a plan for the trip, with fixed dates and booked accommodations.
Für die Reise haben wir bisher nur die Idee, mehrere Küstenorte zu besuchen.
So far, we only have the idea of visiting several coastal towns on the trip.