- is to offer the tired person water
You are tired, drink some water.
- is to tell the person to drink some water.
However, if the sentence is accompanied by another sentence indicating water being served to the tired person, then it would mean the same thing as 'have some water'
take water is... not the right way to say it.
have and drink would mean different things.
(i notice that in many ex-british colonies, people use 'take', even older generation Singaporeans, and many Indians... eg, take breakfast, take milk, take coffee... did it come from 'to partake of'? anyone knows?)