When you speak out, you boldly and forcefully say exactly what you're thinking. If activists didn't speak out about injustice, discriminatory laws would never be changed.
When people speak out, they let their voices be heard. A protester might speak out about her opposition to a government's policies, and a teenager might speak out to his parents about his entirely unfair curfew. In both cases, people are direct and open about how they feel and what they believe to be true. You could also say they speak up or say something loud and clear.