I have an arrangement with my neighbour (not plan): we bought a lawnmower together to cut the grass in front of our houses; the last person to use the lawn mower cleans it and stores it away until the other needs it. I have a plan (not arrangement) to cut my grass next weekend. (other contexts are possible... - sometimes these two words can be synonymous...)

Hi Lilith! They are quite similar words! Arrangement can be more formal and business-like. Plan sounds a little less formal - we might say to our friends 'What's the plan for today?' But we would also use plan for some kind of evil or criminal scheme. "The robbers' plan was to break in to the bank at midnight."