The reasons that I explore such a question is to help people in organisations cut through the verbiage of 'management' books that cover these terms.
The difficulty that I have with the 'answer' given here is that the referents (rather than definitions) given for each word can be interchanged and still hold the same general meaning. Purpose, aim, goal &c are all "something that you want to achieve when you do something: "One purpose of the games / one aim of the games / one objective... is to have an educational purpose."
an "aim" is a broad statement of intent: to provide employment... / to reduce poverty / to increase profits / to halt the flow of drugs &c. (It may be likened to a wish, a prayer or a hope.) E.g. "I am going to learn to drive"
a "goal" is a slightly more detailed statement: to increase employment to 90% / to reduce poverty by 1/3 / to increase profits by 10% / to halt the flow of drugs to juveniles &c. E.g. I am going to learn to drive a car as soon as possible."
an "objective" is a PRECISE (unambiguous) statement of a set of REALISTIC and MEASURABLE targets to be achieved. E.g. "I am going to go to the ABC school of motoring tomorrow morning and sign on for a set of lessons costing not more than £250 with a view to passing my test within one month of starting the lessons." This has [Measurable] targets of Quality (pass the test); Quantity (set of lessons / 1 test) Time (tomorrow, AM / 1 month) and Cost (£250) it is KNOWN, UNDERSTOOD and ACCEPTED by the person involved and so it meets the PRAMKU test for an objective.
"Purpose" seems to relate more to the broader reason for existing E.g within which Aim &c are the statements indicating how this is to be achieved.
"Ambition" seems to relate to a personal aspiration E.g. My ambition is to be a Rock Star"