There is a significant amount of overlap between justice logos and legal logos. Many of the same symbols are used, and a law firm might think of their logo design as both a legal logo and a justice logo at the same time.
However, there are some organizations that focus specifically on justice rather than on the practice of law, like the many groups that fight for social justice or civil rights. These organizations may want to avoid the use of symbols associated with legal logos to limit confusion regarding their mission and activities.