I had a manager once who argued that there was no difference between influence and manipulation. He was one of the most manipulative people I've ever worked with, and working with him was very obnoxious and stressful. I suspect most people who argue that there is no difference are either very manipulative people trying to justify their own behavior, or are people who have been taken in by such people.

IMO people get too caught up in the words "influence" and "manipulate", and effectively start arguing over definitions (whether they realize that's what they're doing or not). I don't think any of that matters.

What matters is whether you're behaving like a decent human being who respects and cares about others. The negative things that people associate with the word "manipulate" are things like trickery, dishonesty, etc. As long as you are approaching others with respect, authenticity, honesty, and a reasonable amount of humility, then I don't think you need to worry about whether your influence counts as "manipulation" or not: you'll be avoiding the aspects of "manipulation" that make it a bad thing.