Short answer: no.
Ramadan and Eid are not the same. However, they are both celebrated by Muslims. Ramadan is known as the Holy month when fasting occurs. Muslims will abstain from eating and drinking for the month. Eid (Eid al-Fitr) on the other hand, is when the month-long fast is finished and Muslims come together to celebrate. Eid al-Adha occurs during the end of performing Hajj, i.e. the pilgrimage to Mecca.