Isn't "茶水" tea too?
茶 refers to "tea", whereas 茶水 refers to "tea" (liquid). They both have the same meaning. However, 茶 is commonly used since it's short-formed term.
So whats i want to drink tea or do you want to drink tea?
I want to drink tea = 我要喝茶 （Wǒ yào hē chá）
Do you want to drink tea = 你要喝茶吗？（nǐ yào hē chá ma?）
茶水 cháshuǐ = tea prepared with boiled water
茶 chá = tea plant - tea (like above) - tea drink
As you see, the first one has a more specific meaning than the second one, which can be referred to more things. So your solution is correct, too.