No! You don't have to be a Muslim to be a terrorist. You just have to be crazy enough to want to force your views on others. Terrorists use different reasons to justify their actions. It could be religious, cultural, Political or just psycho.
The two are very distinct terms.
Muslim: A person who practices the religion of Islam. The religion entails, for the pious worshiper, praying five times a day; observation of holidays like Ramadan, Eid ul-Fitr, Eid al-Adha, and Awwal Muharram; a pilgrimage to the holy site of the Kaaba in Mecca once in one's life; and, most importantly, proclaiming the Unity of God. Unfortunately, not all Muslims practice their religion as perfectly as one would like, resulting in Muslims who do not follow all of the tenets of Islam. A small minority of these individuals use their apparent faith as a cloak for whatever misdeeds they wish to perform for whatever injustices they believe they have suffered.
Terrorist: A person who uses a violent act to instill fear in a civilian population, usually to achieve a political goal.
Certainly Muslims can be terrorists, since all Muslims are people. On the same token, Jews, Christians, Atheists, Buddhists, Hindus, and all other types of people can be terrorists as well for the same reason. However, not all terrorists are Muslims and an incredibly small percentage of Muslims are terrorists. The problem is that fear spreads quite quickly and a vocal minority can usually out-speak a substantial moderate majority.