If you speak "out loud", then you are saying something for everybody else to hear instead of just thinking it to yourself or saying it very quietly just to yourself / people close to you. If you are speaking loudly then the volume of your conversation is (too) loud instead of quiet or normal volume.

Speak loudly, is raising the volume of your voice when you are speaking. Speak out loud, is for example if you are reading in your head and someone tells you to speak out loud, that means you read with your voice. So speak out loud means, to actually speak, rather than speaking in your head.