Difference between Hady and Udhiyah

There is a big difference between hady and udhiyah.

The hady is a sacrificial animal immolated in the name of Allah by the pilgrim. It is to be slaughtered in Al-Haram and distributed among the poor and the needy. The hady is offered in certain cases, among which is the tamattu` Hajj (in which the pilgrim performs `Umrah, gets out of the state of ihram, and then enters ihram again for Hajj). This is indicated in the Qur’anic verse in which Allah Almighty says: “If any one wishes to continue the `Umrah on to the Hajj, he must make an offering, such as he can afford” (Al-Baqarah 2:196).
If the pilgrim cannot afford the hadi, then he can do what Allah Almighty has mentioned in the same verse, when He Almighty says: “but if he cannot afford it, He should fast three days during the Hajj and seven days on his return, making ten days in all” (Al-Baqarah 2:196).
As for the udhiyah, it is a sacrificial animal that a Muslim slaughters on the Day of `Eid Al-Adha following the Sunnah of the Prophet (peace be on him). The udhiyah is to be divided into three thirds: 1) one third for the person and his family, 2) one third for the relatives and friends, and 3) one third for the poor.