Terrorists specifically hold people as hostages to gain the ultimate power in decisions being made. They also kill people on a random basis to instill terrifying fear into the remainder of the family, group, nation, or power bloc. The Nazis used refined terrorism via the Gestapo. The Gestapo would kill dozens and even hundreds of unarmed civilians simply as a warning against trying to oppose the Nazis.
On that basis, neither America nor Israel are currently terrorists, with their actions designed to destroy Islamic terrorism promoters. They are reacting with long-held hatred from previous terrorism attacks against them by Islamic terrorists, to destroy those Islamics they see as promoting terrorism against the West, and against the State of Israel.
But both America and Israel have utilised terrorism in the past. The State of Israel was founded on terrorism of the British (and the Palestinians), and specifically by acts of terrorism by the Zionist Stern and Irgun gangs.
American terrorism acts were were funded and encouraged by the CIA, often employing locals they'd trained. In places such as the Middle East, South American countries and Asian countries, where unstable Govts or dictators who were seen to be rabidly anti-American, the CIA set out to create disruption, cause regime collapse, and even carried out political killings.
The assassination of President Ngô Đình Diệm in South Vietnam in 1963, by a group of Diệms army officers, was actively encouraged, funded, and supported by the CIA.
Further back, the Americans killed a lot of Native Americans in what was essentially acts of terrorism, designed to acquire their lands and resources. The Wounded Knee Massacre is possibly the worst example of Americans killing unarmed or disarmed Native Americans.