Extremism and terrorism are both vigilantes in nature, i.e., their political actions are excessive and also commit politically violent actions. Thus not all political extremists are terrorists, yet some are terrorists. That is to say, most political extremists are law-abiding citizens whose beliefs might be extreme; however, they do not resort to violent acts to achieve them. You may say the actions of some factions of the current tea party movement are extremists but they are not necessarily terrorists. However, the anti-government militia Hutaree who were planning to murder police officers are domestic terrorists.
Nonetheless, all terrorists are political extremists because they commit acts of violence to achieve their political goal(s). Terrorists can be grouped as left-wing terrorists who are political radicals in nature and whose goal is to reform or overthrow the established governmental order for the greater freedom of the common man. They can also be termed are right-wing terrorists who are political conservative and whose goal is to restore or maintain the established governmental order. These are the traditionalists.

And lastly, we have the special interest terrorists who are either left-wing terrorists or right-wing terrorists, who commit violent acts to address a specific cause or issue(s); such as, to promote active participation of disfranchised societies through the resolution of existing problems including racism, poverty, unemployment, social injustice, freedom of speech, and fighting against Statehood and advocating for Independence (e.g. Puerto Rican Independistas, Jewish Defense League, Student for Democratic Society, etc.).