A ‘Eid is a day of festivity that is repeated on a specific day/night. That can be yearly, but it can also be weekly; Yaum al-Jumu’ah for example. The total number days of ‘Eid are counted to a maximum. You may not add to it or decrease it, except with evidence. والله أعلم
I will cite a hadīth wherein the noble Prophet of Allāh صلى الله عليه وسلم uses that word (‘Eid):
 ‘Uqba bin ‘Āmir narrated that the Messenger of Allāh صلى الله عليه وسلم said: “The Day of ‘Arafah, the Day of Nahr, and the Days of Tashriq are ‘Eid for us; the people of Islam, and they are of eating and drinking.” (Hasan)
Abu ‘Eisa (al-Tirmidhi) said: There are narrations on this topic from ‘Ali, Sa’d, Abu Hurairah, Jābir, Nubaisha, Bishr bin Suhaim, ‘Abdullāh bin Hudhāfah, Anas, Hamzah bin ‘Amr al-Aslamī, Ka’b bin Mālik, ‘Ā-isha, ‘Amr bin al-‘Ās and ‘Abdullāh bin ‘Amr.
Abu ‘Eisa said: The Hadīth of ‘Uqba bin ‘Āmir is a Hasan Sahīh Hadīth. This is acted upon according to the people of knowledge. They consider it disliked to fast on the Days of Tashriq, except that there are those among the Companions of the Prophet صلى الله عليه وسلم , and others, who permitted it in the case of the one performing (Hajj Tamatu’ – if he did not find a Hadī, and he did not fast during the ten (days) – then he can fast the Days of Tashriq.
This is the view of Mālik bin Anas, Ash-Shafi’i, Ahmad, and Ishāq.
Abu ‘Eisa said: (Regarding one of the narrators:) The people of al-‘Irāq say: “Mūsā bin ‘Ulayy bin Rabāh” while the people of Egypt say: “Mūsā bin ‘Ali.”
He said: I heard Qutaiba saying: “I heard al-Laith bin Sa’d saying: ‘Mūsā bin ‘Ali said: “No one has been given the liberty to pronounce my father’s name in the diminutive.'”
 That is to say: ‘ulayy rather than ‘Ali.
Source: Jami’ at-Tirmidhī, 2/204-205, The chapters on Fasting, Chapter 59. What has been related about it being disliked to fast the days of tashrīq, darussalam — See further: Abu Dāwūd: 2419, al-Nasā-ī: 5/252, Al-Kubrā: 2829, Ahmad: 17379, Hākim: 1/434.
وَمَن يَتَعَدَّ حُدُودَ اللهِ فَقَدْ ظَلَمَ نَفْسَهُ
Translation: “…Who transgresses the limits of Allāh, does verily wrong his (own) soul…” [65:1]