You would 'sound out' somebody (or a group of people), or you would 'run it by' somebody (or a group). They are very similar in meaning, but to a native speaker I would say that 'sound out' indicates a slightly more serious or thorough procedure. If I were going to make a major change in the workplace, I would 'sound out' my managers and colleagues for their views before doing so. If I were going to make a less serious change that I thought would be approved, I might just 'run it by' my manager before doing so. The presumption is that everything is probably okay, and running it by them is just a quick formality or courtesy. Does that make sense?

The correct expression is "run something by someone" https://idioms.thefreedictionary.com/run+something+by+someone Yes, there is a difference. When you sound out people, you actively seek their opinion. This is the figurative meaning of "to sound", in the sense of finding the depth of water. When you run something by people, you give a short explanation or demonstration of your idea. It's a presentation, and you are looking for their impressions or reactions. You don't always need detailed feedback.