“Accolade” is more neutral, formal between two persons.

“Câlin” is more signifiant for two people who have a more strong connection, like two friends or two lovers.

“étreinte” is more related to lovers, like a hug that last longer.

So yes, it is more like you were thinking 😉

Accolade originally means a hug where you hold the neck of the other person. In accolade there is col which is (with cou) the word for neck.

But accolade usually means some kind of formal hug between two people, eg. politicians.

Accolade is also the French for curly brace.

Câlin indeed involves some kind of tenderness. Câlin applies to : a mom to her child, a kid to his teddy bear, friends or two lovers.

As for étreinte, there is a notion of strength or a lack of equilibrium between the people involved.

Étreinte can describe something wilder, and sometimes unwanted. You would use the word for a wrestler holding his opponent for example. It also means a passionate hug.

accolade
câlin
étreinte

accolade is somewhat literary or formal. It means to embrace in a way that involves the neck.

câlin is what parents do with children. They cuddle them. The expression is faire un câlin. It can also be translated as: to give hugs to someone or physical affection.

étreinte is usually associated with a close embrace that lasts longer than a simple hug and does not necessarily involve the neck. It is often associated with an embrace associated with sexual relations. The lovers clasped each other tightly. Les amants se tenaient par une forte étreinte.

But it can also be used in a negative way:

Il n’arrivait pas à s’échapper de l’étreinte de son ennemi. He could not escape his enemy’s grasp. And also means grasp in the sense of being held by something or someone one wishes to escape from.