To request someone to come to an event or a place.

बुलाना

English Usage: I would like to invite you to my birthday party.

Hindi Usage: मैं आपको अपनी जन्मदिन पार्टी में बुलाना चाहता हूँ।

To request someone to go out for an activity such as dining or entertainment.

बाहर बुलाना

English Usage: He decided to invite her out for dinner.

Hindi Usage: उसने उसे रात के खाने के लिए बाहर बुलाने का फैसला किया।

A written or verbal request inviting someone to go somewhere or to do something.

निमंत्रण

English Usage: I received an invitation to her wedding.

Hindi Usage: मुझे उसके विवाह के लिए निमंत्रण मिला।