What is the difference between those two ways of saying "to want"?
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The 〜たい -tai form attaches to the masu-stem of a verb to form "to want to [verb]", e.g. 食べたい tabetai "to want to eat". The form したい shitai is only the special case of 〜たい attached to する "to do". Even though it attaches to a verb, the result is an i-adjective (unlike in English).
(が)ほしい comes after a noun and means "to want [to have/own] a/the [noun]". Like practically all words ending in しい, it is an i-adjective as well.
(～て)ほしい may also come after the te-form of a verb and means "to want so. to do [verb] [for me]", for example 食べてほしい "I want so. to eat [this]".
In general, these constructions are different, but in case the verb is a "suru-verb" (i.e. of the form [noun]+suru) they may appear similar. However, they usually do mean something different:
denwa (wo) shitai
I want to make a call / I want to call [so.]
denwa ga hoshii
I want [to own/to have] a phone
denwa (wo) shite hoshii
I want you to make a call / I want you to call [so.]
shitai n desu ga
I would like to do [sth.]
hoshii n desu ga
I would like to have [sth.]
shite hoshii n desu ga
I would like you to do [sth.]
Note that both 〜たい and 〜ほしい express your own desire/wish. According to the unwritten rule that you cannot know the details of a third person's mental state, you should use 〜たがる and 〜ほしがる instead if you want to talk about the desires/wishes of other people. For more on this see the following questions:
You must mean shitai(ndesu)
The difference between hoshii ほしい shitai したい is that one is for when you want to do something, and the other is for wanting an object
hoshii is an adjective. It is commonly used with the subject particle ga が to say that you want something. For example
りんごがほしい (ringo ga hoshii) I want an/the apple
It can only be used with nouns, as it is an adjective describing the noun as 'desirable'.
The -tai ending is attached to the stem of a verb (the part before 'masu'), and it expresses that you want to do whatever it is that the verb refers to. For example
サッカーをしたい (sakkaa wo shitai) I want to play soccer
Here, shitai means 'want to play'. The -tai ending can be attached to any verb.
りんごをたべたい (ringo wo tabetai) I want to eat an/the apple
A somewhat similar meaning to the hoshii sentence, except that hoshii does not imply what you would do with the apple. Tabetai clearly expresses a desired action.
Hoshii can also be used, when you wish to express that you want someone else to do something
It is attached to the -te form of the verb. For example
りんごをたべてほしい (ringo wo tabete hoshii) I want you to eat the apple
The '-ndesuga' ending is a separate issue, but essentially it makes what you are saying a little bit less direct. As a basic sentence, you don't need it.
欲しい and たい are adjective, and DOES NOT mean “I want”.
They mean “is desirable”
The apple is desirable.
Same concept applies to たい.
Please people stop making people thinking that 欲しい means “I WANT”. It doesn't mean that. The subject is the the desired thing, and the adjective means that it procures desire to you.
The book procure to me the desire to read it
Japanese is not ego-centric like English.