They are slightly different but people will still understand you if you mix them up. I found the following definitions which may help. 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.

To achieve means to reach a target. Whereas to accomplish means to complete a task. For example, a student who has studied for their exams will hopefully 'achieve' good grades. However, a worker who is working hard will hopefully 'accomplish' a lot today.