In general, aim, goal, objective can be considered synonyms, but...

Case by Case

Purpose

What you want to achieve when you do something
The reason you do or plan something
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.

To make it more clear

Aims tend to be more general, vague, non-specific, long-term, compared to
Goals, which are more likely to be specific, short-term targets
Objectives are somewhere in between, or more accurately, they simply have no relationship with this distinction

Thus, it is more likely to have a

long-term strategic aim/objective

which is broken down into component goals

in pursuit of that aim, rather than a goal which is achieved by meeting several subsidiary 'aims.
Regarding the point about goals being more associated with short-term aims,

It is worth pointing out that a goal in ball/puck game contexts (soccer, say) is just one step towards the aim / objective (to win the game). A bit like Winning the battle not the war.

Tip

In the context of a resume or curriculum vitae, I'd probably use objective, if for no other reason than it sounds a bit more formal/professional.