I think both of you have missed the point of the slogan. Ask yourselves: what is the opposite of peace?

These people are making a threat.

Notice that in both cases, what is demanded is “justice”. That’s a wonderfully vague and squishy word that means whatever the speaker wants it to mean. Consider, for example, the concept of “social justice”, which really means “taking money away from people I don’t like at gunpoint and giving it to people to people I do like.” In other words, the exact opposite of what “justice” has traditionally meant.

“Justice,” in this context, is a code word for “whatever I want.” “No peace” is a code phrase for unspecified violence. And the slogan “No justice, no peace” simply means “Give me what I want or else.”

“If you want peace, work for justice” is just a slightly different wording. The meaning is the same.