Difference between "get" and "take"

In my sense, take will denote some action from the subject, whereas get is more passive.

"I take from you. You get from me."

The first sentence would be construed as I don't require your permission to 'get' something. The second sentence would mean that unless I give, you cannot 'take' something.

'Take' would seem authoritative when used in a 'person as a subject' setting.

It depends how you use the two words. The both words can be used as passive or active verb depending on the situation.

Let's look at this example: My boss asked me to (take, get) the office key from his office assistant. Here, if you use (take), your expression may sound harsh.

Example 2: The detective (got, took) the suspect by force as he left the restaurant. In this example, either of the two verbs in the parenthesis are correct.

There is two words of same meaning that is "take" & "get". Mostly, words "take" is use to be for take something hard. For example, take my pen. Whilst word "get" is to be use for get permission from someone.

"Get" also means to go and "fetch" something then bring it back to where you currently are.

You left your book in your locker? Go get it.

"Take your book" would be to grab it and go elsewhere, like from home to school.

Given that both take and get have many uses and idioms, the short answer is: When talking about movement take is usually away, and done by the speaker. Get is usually towards and often done by someone else. For example I get groceries from the store. I take them home. Or with an example like "I take a taxi." or "I get a taxi." They mean practically the same thing. But the first emphasizes the fact that you will go by taxi. Getting a taxi emphasizes the act of calling a service to have someone bring a taxi. (that you then take to a destination.) When discussing acquiring things, take emphasizes the act and can be with or without permission. Again, the subject is doing the taking. Get implies permission and often that someone else is doing the giving. An Example is an adult walks into the break room and takes a cookie. (maybe he had permission, maybe he didn't. we don't know.) He tells his son, "If you are good you will get a cookie." The kid will have explicit permission to receive the cookie and likely someone else will give it to them.

Keep in mind that get can also mean to become or to understand. And take is used in several idiomatic expressions like, "My take" which refers to your opinion. Because English is crazy like that. ;-)