Which one of the these is the correct, or can I use both?
- take a rest
- have some rest
Or is there any better way to say that?
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In my (UK) idiolect "have a rest" and "get some rest" are idiomatic, not the two phrases you give.
I find a slight difference in meaning. To me, "have a rest" is neutral: I am going to rest, with no implication about how much I need it.
"Get some rest" implies that I have a particular need for rest: either I have been short of rest recently, or some major activity is expected so that I need to be well-rested before it, or there is very little time available for resting, so I will avail myself of it.