Fellow Lemmings, in work-place conversations (like conflict resolutions, negotiations etc), where you feel you are being misunderstood, how do you manage to realign the conversation?

Well use a medium where you communicate better. Many can articulate better with the written word. Try continuing the conversation over text or email or whatever.

Pro tip: if you own your mistakes and never try to hide or diminish your responsibility, it's like a secret weapon to diffuse blame. People will accept that you made a mistake and just move on.

Flow charts or bullet lists as visual aid. The higher position your interlocutor is in the simpler you should try to keep your point. If you need their input on a project only bring them one A vs B decision at a time.

Ask questions, like "How did you interpret what I said?". Neutral and always non-confrontational. Make sure it's an open question, so no yes/no answers.

That will help you understand their thought process and figure out a more effective way to explain yourself to that person. Maybe even in general.