It’s happening throughout the media, but The New York Times characteristically has some of the best examples.
Where it comes to Palestinians, armed groups that attack civilians are termed “militant” groups and the adjective “terrorist” is regularly used to modify uses of the noun “attack”:
For its part, Israel continued its policy of targeted killings when an army helicopter fired missiles on a farmhouse in the West Bank town of Bethlehem, killing four men, two of them described as senior figures in the militant Islamic group Hamas. Late tonight the Israeli Army sent infantry and armored reinforcements to the West Bank.
Palestinians called the Bethlehem killings an assassination. Israeli officials characterized them as an “interception,” saying the Hamas men had been planning a major terrorist attack soon in nearby Jerusalem.
—from “Anxiety Rises After Attacks In West Bank And Israel,” by Clyde Haberman, The New York Times, 17 July 2001.
When it comes to armed Jewish groups attacking civilians, however, the rules change slightly, and attacks are never described as “terrorist”:
Three Palestinians, including a baby, were killed tonight west of the West Bank city of Hebron in a drive-by shooting that the police said was apparently an attack by Jewish gunmen.
The Committee for Security on the Roads, a group of militant Jewish settlers in the Hebron area linked to the banned anti-Arab Kach movement, claimed responsibility. But the police said it was not yet clear which group was behind the attack near the village of Idna.
—from “Three Arabs Slain; Jewish Settlers Claim Responsibility,” by Joel Greenberg, The New York Times, 19 July 2001.
The term “terrorist” is only applied by The New York Times to Palestinians in the conflict. Lest the paper’s journalists are blamed solely, we should note that this also holds true for editorials, eg. “Fragile Cease-Fire in the Mideast,” The New York Times, 5 June 2001 and elsewhere.
When reporting the 19 July 2001 Jewish settler shooting of three Palestinians, including a three-month-old baby, not only do we not see the attack described as “terrorism” by The New York Times, but the perpetrators are described as “vigilantes”:
For days, Israelis have been holding their collective breath waiting for a reprisal attack after a drive-by shooting, presumably the work of Jewish vigilantes, that killed three Palestinians, including a 3-month-old boy.
— from “Sharon Booed by Fellow Rightists Who Say He’s Too Soft,” by Clyde Haberman, The New York Times, 23 July 2001
As far away from “terrorist” as white is from black, the word “vigilante” has an implicit justification. Merriam-Webster dictionary defines vigilante as:
A member of a volunteer committee organized to suppress and punish crime summarily (as when the processes of law appear inadequate); broadly: a self-appointed doer of justice
Although the use of the adjective “vigilante” is unlikely to be intended by any journalist to imply that killing three Palestinians — including a baby — on their way to a wedding party is an act of ‘justice’, their inappropriate use of this word does make it obvious that many journalists shy away from applying the adjective “terrorist” to Jews or “Israelis” but do not apply the same restraint when writing about Palestinians.
This is racism, pure and simple.