I have heard JWs say that a "plan" suggests that it could possibly be changed or even foiled by someone other than its designer.
And that a "purpose" cannot be changed or aborted, except by the designer.
You "purpose" to build a house, though, your specific architectual "plan" for it may change a few times before you actually complete your "purpose" of building a house.
In JW language......... Jehovah's "purpose" is for obedient humans to live forever in Paradise Earth. How Jehovah accomplishes could be in several different ways..... 1.) Just create one man & one woman to populate and care for the Paradise Earth, happily ever after. 2.) Resurrect only natural born Israelites to heaven in rule and help manage humans the Paradise Earth. 3.) Resurrect a variety of 144,000 Christians to heaven, kill off all the bad people and then help rule and manage the obedient survivors in a Paradise Earth. Or 4.) Just start all over again. Whatever the case may be........ Jehovah's "purpose" will never change..... that of obedient, perfect humans living forever in a Paradise Earth........
When I read the definitions of the two words in English dictionaries, they appear to share almost the exact same definition.
So, unless there is some specific difference in the original Hebrew/Greek words for "plan" and "purpose", which there may be, it seems to be just another typical JW opinion on word definition.