Wish and hope followed by infinitive

As many know, when followed by a clause, 'hope' is used to express a event
that is real, possible but 'wish' to express a event that is unreal or impossible
or express regret. In other words, 'hope' is used for first conditional sentence
and 'wish' for second and third conditional sentences. For example,
1. I hope that I will be a millionaire (hopeful and possible)
2. I wish that I would be a millionaire (hopeless and impossible)

However, if followed by infinitive, i.e.
1. I hope to be a millionaire
2. I wish to be a millionaire

Are there any differences between them?


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