The goal, the need, the truth, and the lie
I will interpret the character's needs as something they objectively need, if they understand it or not.
I will deal with wants and desires at the very end.
In most cases, the main character follows a positive change arc. This means they believe in the lie of the story and will, at the end of the story believe in the truth instead.
They have gone through an arc or a change.
The lie and the truth can be anything. Killing, stealing, cheating is justified. Or not. The law is right. The law is corrupt. Etc.
It usually ties into a theme that will create a packaging or grouping of lies and truths... and generate different variations of them for different constellations of characters and subplots etc. Most commonly for the hero and the villain.
E.g. a theme about killing, with a lie that killing in anger is ok, and a truth that killing in self-defense is ok.
Since the main character believes in a lie at the beginning of the story, they will have formulated a plan/have a goal, that is bad for them (that supports a lie).
If this goal is not present at the very beginning of the story, it will usually be triggered during or at the end of the first act.
If, for example, the lie is that money makes you happy and the truth is that people make you happy, the goal of your main character might be to earn money, while what they need is to nurture their relationships.
To make a story great, put the goal and the need diametrically opposite each other.
Your main character's goal to make money is so intense it pushes people away, even hurts them... and, even better, if that money-grabbing also hurts the main-character themselves as well.
He wants money (see the end of the answer for details). But he needs people.
Maybe he's at risk of failing as a parent if he pursues his goal of money-grabbing and he will neglect and alienate his children.
And he needs his children.
The motivation and the backstory
The motivation is usually rooted in some or several of backstory, emotional wounds, psychology, politics, religion, etc.
It answers the question of why the character has his goal.
Say for instance that your main character was really poor as a kid, maybe someone even died from malnutrition. This would be an emotional wound that would make the character feel an urgent need to, above all else, make money.
When confronted by his kids about being neglectful, this will be very hurtful. He is fighting like hell to save them from the horror of poverty, even from death and the spoiled brats are whining about a day at the zoo? WTF?
Notice how the motivation and the lie interact here? Is the lie still "Money makes you happy" or is it "without money you die"...? Which one is more dramatic? Which one does the father tell his children to protect them from his past?
Now you have conflict... and a grand task of making that parent (he was supposed to follow a positive arc, right?) understand the perspective of his kids... or maybe they all need to understand one another...?
We don't really have a villain here, do we? If you let your readers know from the start all the motivations and all the backstory and everything else...
...which of course you don't. You should be cautious about backstory too early in the story—because your readers don't know your characters yet and don't care too much about their past... they want the action of now.
You should also be cautious about giving your readers, and your characters, total understanding of all motivations, and needs, and desires, etc. If you do there won't be much conflict, will there?
You'd better hide, conceal and fudge about the backstory and the wounds and all that for a while. Maybe the parent will not go all out about his horrible past until in the huge fight at the very climactic moment of the story. (I define the climactic moment as the very last scene of conflict—and pretty much one of the last scenes in the whole story—anything that comes after is mop-up, reconciliation, and perhaps a pinch of showing the new normal).
Your main character may not even understand that he is money-grabbing due to his past. He may not want to think about it, being poor and all, now that he's a prosperous member of society?
But of course, he loves his kids and of course, he cannot live without them, so... he and everyone else is in for a ride...
Wants and desires
In the context of story-building wants and desires are, in my opinion, more about the psychology of the character's decision-making.
They can, for instance, be used to set up the stakes or show the conflict between the character's goal and what the character needs.
In the beginning goals, wants and desires are all aimed at money.
But then the kids enter with their demands for a parent, and things shift. The main character might yell at the kids that they are spoiled and ungrateful, but he wants and desires to be a good parent, why else would he fight so hard to get money to protect them?
If he listens to the wants and desires for money he will alienate his kids, and if he listens to the wants and desires to be a good father he might risk having the kids starve to death...
Maybe it's time for a mentor to enter the stage and offer some help and incentive to change... some sober perspective of the risk of starvation and death?
Linguistics and Language
From a language perspective, it's fine to say that the main character wants, desires, or needs money, or that he wants, desires, or needs to be a good parent, or that he wants, desires, or needs to avoid being poor again.
The words could all be used for needs, goals, and motivations.
That's how language works. However, what I've described above are more "functions" in a story and a character that will help structure conflict and motivation.
It's perfectly fine to have the character thinking that he needs money. Then it's a measure of the strength of his desire. I think need is stronger than want or desire.
As long as the author knows that what he needs, rather than reaching his goal is to save his relationship with the kids.