This is true. Israelis want “peace”. Palestinians want “justice”.
If you take a good look at Israeli culture and history, you will find that the majority of those who used to wish for peace (nowadays nobody believes it will come) didn’t do it out of a sense of guilt, or a desire to atone for crimes. They wished for it because they were tired of fighting and killing and dying. Also, most Israelis didn’t differentiate between peace with the Palestinians and peace with other Arab countries. It was all part of the same conflict. The utopian dream of peace included visions of “eating hummus in Damascus”, a phrase that became a metaphor about the longing for a cessation of violence and normalisation of relations.
After the signing of the Oslo Accords, the Israeli public became drunk on the hopes for peace (see, for example ‘Shir LaShalom’ [A Song for Peace] that was very popular in that era). The disillusionment came only with the second Intifada, when the Israelis realised that the Palestinians weren’t about to end the conflict or give up the right of the refugees and their millions of descendants to return to Israel.
Now only Haaretz is still talking about peace.