κάτι = something
It is used in statements or questions
Θέλω να φάω κάτι. = I want to eat something.
Χρειάζεσαι κάτι; = Do you need something?
τίποτα = anything
It is used in questions or negative sentences.
Σου έδωσε τίποτα; = Did he give you anything?
Δε θέλω τίποτα. = I don't want anything.
κάτι and τίποτα can be used interchangeably only in questions and negative sentences, but not in statements.
Θέλεις κάτι; = Θέλεις τίποτα; = Do you need something / Do you need anything?
Δε θέλω κάτι. = Δε θέλω τίποτα. = I don't want something / I don't want anything.
The second version of the negative sentence (δε θέλω τίποτα) sounds more natural in Greek than the first one (Δε θέλω κάτι).
The phrases "Δε θέλω κάτι" / "Δε θέλω τίποτα" are correct and they mean "I don't want something" / "I don't want anything" respectively.
The phrase "Θέλω κάτι" is correct and it means "I want something".
The phrase "Θέλω τίποτα" is wrong.
The correct version is "Δε θέλω τίποτα". (we need to add the negative word δε / δεν)