These words are pretty similar and have only subtle differences and in spoken language many people might not be careful enough to use each of the words correctly. However I think the explanation from Longman Activator Thesaurus is quite helpful:
Purpose: what you want to achieve when you do something; the reason you do or plan something, and the thing you want to achieve when you do it: The games have an educational purpose.
Aim: something you hope to achieve by doing something: The main aim of the plan was to provide employment for local people.
Goal: something important that you hope to achieve in the future, even though it may take a long time: The country can still achieve its goal of reducing poverty by a third.
Target: the exact result that a person or organization intends to achieve by doing something, often the amount of money they want to get; a particular amount or total that you want to achieve: The company is on track to meet its target of increasing profits by 10%.
Objective: the specific thing that you are trying to achieve – used especially about things that have been officially discussed and agreed upon in business, politics, etc. and agreed upon in business, politics, etc.: Their main objective is to halt the flow of drugs. | We met to set the business objectives for the coming year.
Ambition: something that you very much want to achieve in your future career: Her ambition was to go to law school and become an attorney. | Earlier this year, he achieved his ambition of competing in the Olympic Games.