According your description you seem to have prayed the first time a Eid prayer.
The major difference between Eid prayers and Jumu'ah is that the sermon of the Eid prayer is performed after the prayer, while in Jum'ah it is done prior to the prayer this is the sunnah. Some sunni reports say that Marwan tried to change it because people were leaving the prayer place after he lead the prayer, but the sahaba refused to change the sunnah (see in sahih al-Bukhari and sahih Muslim)!
The other difference to any other prayer is that following the recommendation of the Prophet () to perform takbir during the day of Eid and the days of tashreeq (11th, 12th, 13th dhil Hijja) and that also being a sunnah we add some additional takbirs in the standing positions right before reciting al-Fatiha.
The madhhabs have different amounts which they consider sunnah based on different tradtions.
Here just a quote from your linked Wikipedia article:
Performing Eid-ul-fitr prayer
Eid al-Fitr prayer (Salat al-Eid) or Eid al-Fitr Namaz is performed on the occasion of Eid. The Prayer of Eid al-Fitr is performed in two different ways by Sunni and Shia Islam.
There are two Rak'ah (Rakaat) performed in the Eid al-Fitr prayer. The prayer of Eid al-Fitr starts by doing "Niyyat" for the prayer and then Takbeer (Allahu Akbar) is said by the Imam and all the followers. The next is to recite "Takbeer-e-Tehreema" in first Rakaat. Then the congregation says Allahu Akbar seven times, every time raising hands to the ears and dropping them except the last time when hands are folded. Then the Imam reads the Surah-e-Fatiha and other Surah. Then the congregation performs Ruku and Sujud as in other prayers. This completes the first Rak’ah. Then the congregation rises up from the first Rak'ah and folds hands for the second Rak’ah. In the next step the Imam says five takbirat, followed by the congregation, every time raising the hands to the ears and dropping them except the last time when the hands are folded. Again the Imam reads the Surah-e-Fatiha and another Surah followed by the Ruku and Sujud. This completes the Eid prayer. After the prayer there is a khutbah.
This shows only the majority madhhab view or follows the description of Sayyid Sabiq's fiqh as-Sunnah, where he also quotes that hanafis perform three additional takbirat at the first rak'a (p.150 Volume on supererogatory prayers)!
The details on takbeer during the Eid prayer from the sunni perspective:
After takbirat al-Ihram (takbir at the start of the prayer) three takbiraat!
After the takbir to start the second rak'a again three takbiraat!
This is also one of two statements of Imam Ahmad!
This is based on narrations on the authority of ibn Masu'd and ibn 'Abbas which are also held by ibn Hazm in his Mohalla! I'll try to translate:
أنه كبر أربعاً ثم قرأ ثم كبر فركع ، ثم يقوم في الثانية ثم يُكبر أربعاً .
That he made four takbiraat than started the recitation, then he say Allahu Akbar and move to ruk'u and then when he stands up for the second rak'a he performs four takbiraat (Mosnaf abd-ar-Razaaq)
I also found in sunan abi Dawod this statement of abu Musa al-Ash'ary:
Sa'id b. al-'As asked Abu Musa al-Ash'ari and Hudhaifah b. al-Yaman: How would the Messenger of Allah (ﷺ) utter the takbir (Allah is most great) in the prayer of the day of sacrifice and of the breaking of the fast. Abu Musa said: He uttered takbir four times as he did at funerals. Hudhaifah said: He is correct. Then Abu Musa said: I used to utter the takbir in a similar way when I was the governor of Basrah. Abu 'Aishah said: I was present there when Sa'id b. al-'As asked.
Performing seven takbiraat including the takbirat al-Ihram.
In the second rak'a performing six takbiraat including the takbir to stand up to start the rak'a!
References for this view are in al-Muwatta' on the authority of ibn 'Omar () and sunan abi Dawod on the authority of Abdullah ibn 'Amr () and also in sunan abi Dawod on the authority of 'Aisha ()
After the takbirat al-Ihram one performs seven takbiraat.
After the takbir of standing up starting the second rak'a one performs five takbiraat.
This is based on the hadith of ibn 'Omar from above with the notation, that the narrator didn't mention the takbirat al-Ihram, so the amount of takbir is referring to those takbirat after it!
This opinion is also held by ibn Abd-al-Barr and ibn Hazm.
Basically the main view of the madhhab is the same as the maliki view, which is also the opinion of ibn Taymiyyah and ibn al-Qayyim.
Shia also perform two Rak’ah in the Eid al-Fitr prayer. Prayer starts with the Niyyat followed by the five "Takbeers". During every "Takbeer" of the first Rak’ah, a special Dua is recited. Then the Imam recites Sūrat al-Fātiḥah and Surat Al-'A'lá and the congregation performs Ruku and Sujud as in other prayers. In the second Rak’ah again the same above steps (five Takbeers, Sūrat al-Fātiḥah and Surat Al-'A`lá, Ruku and Sujud) are repeated. After the prayer, Khutbah starts.
I'm not qualified to comment on this!