Learn English – “I don’t recommend …” vs “I recommend we don’t …”

They are almost the same usually. Most of the time, "would like to" sounds more calm and fancy to me. For example

I want to be a surgeon

sounds more assertive than

I would like to be a surgeon

So I guess your assumption was fairly on point.

One situation where I see them as crucially different is when asking for something to be done to you, or for you. When using "want to be" it sounds more like a demand and less like a request. If I were the boss of a group working on a project, I could say something bossy, like:

I want to be updated at every step.

Whereas if I am equivalent to the other team members, I would request as such, more politely (I guess a boss can be polite too, though):

I would like to be updated at every step, please.

Below is my previous answer, which was about the wrong thing—I didn't notice the 'be' (sorry) but I think may be useful for some, so I'll leave it.

This is answered in English Language Learners and somewhat here and by many results in a google search.

However, I feel that none of those answers contribute good examples of which context you would use each in. I think this is what makes them the most different—the fact that "would like" sounds more polite in certain contexts, in many of which "want" isn't quite appropriate.

If I'm talking to someone I know, I think the following are equivalent

I want a backrub = I would like a backrub.

In a situation where you're asking for a service or product from a stranger, I would not use "want"

I would like a cheeseburger, please.

I would like more information about this service.

These would sound strange and rude with "want."

Generally, "want" sounds much more assertive too. You could use it when demanding something, instead of asking for it, for example

I want justice!

I want eBay to stop charging me random fees they can't explain.

They mean essentially the same. "Of" is more likely to be used when "break free" is used figuratively to imply freeing something from the influences of something else, while "from" is more likely to be used when physically separating something from something else. But that's not a hard-and-fast rule.