"I want something to drink."
~ほしい expresses your own desire for some object, intangible outcome to someone else. 3 keywords: Your own desire, object, and a listener
~ stem of ます + たい form means you or someone else like to do some action. 2 Keywords: you / others, and action
I like to have [ some ] tea OR I want [ some ] tea
こうちゃをのみたいです I want to drink tea
車がほしいです I like to have a car OR I want a car
車を運転したいです I want to drive a car
Note: ~ほしい can only be used by you to describe yourself, it cannot be used to describe any 2nd person, as it will need a different grammar structure
Stem of ます + たい form can be used either way for yourself to describe yourself, or others, or the other way round, does not need any special grammar
Duo has mistranslated this, the closest sentence would be "I like to have something to drink", since "I like to have a drink" in some cultures or social environments, it would mean you want an alcoholic drink like wine or beer.
Saying "I want ~" may mean similarly, but does not convey the original Japanese meaning of the unspoken understanding that the listener has the option of denying the speaker's request for whatever reason [ politely, of course ] and the speaker himself is mentally ready to have his request denied without hard feelings on both sides