To "take off" in this context means to not go to your job.
To "rest" means to stop working for a period of time.
The ideas are related. Often a person will take off from work so that he can rest.
I can see how reading a definition might be confusing. I carefully used the word "job" above, but we often refer to a person's job as his "work". So you could say that "take off" means to not work, and "rest" means to not work. But we're using "work" here with two different definitions. In the first case we mean "show up at the office or factory where you have a job". In the second case we mean "exert yourself, perform a task which requires effort".
You might take off from work (i.e. from your job) to do a home improvement project. The home improvement might be much more difficult and strenuous than your job, so you wouldn't say you are resting. You can take off but not rest.
Or you could take a break while at your job and rest for a while. Maybe you get a cup of coffee, or chat with co-workers about football. You are not "working" in the sense of exerting yourself, but you are "at work". Or maybe you're just lazy and although you show up at the office, you just sit around and chat on forums. (Oh, wait ...) You can rest but not take off.
Note that "take off" has (at least) two other totally unrelated meanings: It can mean to remove something, often an article of clothing. "Please take off your hat when you enter the building." It is also used to refer to the launching of an airplane or spacecraft. "The airplane will take off in 10 minutes."
No, they are different!
take a look is an idiom which means "to observe or examine someone or something."
On the other hand, looking at someone is merely an act of seeing someone. The purpose of the former one is different.
You look at some product as a normal physiological gesture but if you 'take a look' at the same product, you have a purpose to study/observe it.
Best Answer
There is very little difference in meaning; they are usually just two different ways to express the same thing: someone performed the act of showering.
"She showered in the bathroom" could mean that she regularly or routinely showered in the bathroom; "She took a shower in the bathroom" means that she performed one act of showering in the bathroom.
Take a shower is slightly less formal than shower.
The construction "take a shower" uses take as what's called a light verb in English. A light verb is one that doesn't really carry any meaning by itself, but is used in conjunction with a noun to create a phrase that has meaning. Usually, the light verbs in English are do, take, make, or have.
For example,
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