う・よう + と思(おも)うI think I will, I think I shall, Going to, Gonna (Volitional + と思う)

Both つもりだ and 〜ようと思う・〜おうと思う can both be used to express intentions or plans for the future. つもりだ feels slightly more 'official' or definite, similar to the English 'I intend to' or 'I hope to'. In contrast, 〜ようと思う・〜おうと思う has a more casual and less definitive feel, similar to the English 'I'm thinking of (doing something)'.

〜ようと思う・〜おうと思う expresses intention, similar to 'I'm thinking of doing X,' e.g. 行こうと思います ('I plan to go.') てみる conveys the idea of trying something to see what it's like, e.g. 行ってみる ('I'll go and see.'). These forms can be combined, e.g. 行ってみようと思います ('I plan to go and see what it's like.')

〜よう・おうと思う uses the volitional form with と思う to express plans or intentions, like 'I intend to (A)' or 'I'm thinking of doing (A)' In contrast, plain と思う expresses a simple thought. For example, この本を読もうと思います means 'I intend to read this book.', while この本は面白いと思います means 'I think this book is interesting.'.

Both use the volitional Verb [よう] form. On its own, it expresses a suggestion, e.g. 食べよう ('Let's eat.'). When combined with と思う, it expresses an intention or plan, e.g. 食べようと思う ('I'm thinking of eating.'). The key difference is that Verb [よう] includes others in the action, while ～ようと思う expresses the speaker's personal intent.