Strongly disagree with this sentiment. Influence can have a lot of sources, from institutional authority to simply being persuasive, which is distinct from manipulation.

In this context influence and persuasion are being used interchangeably, but persuasion is the act of winning someone over to your point of view, so they understand the topic as you do. It respects their autonomy and acknowledges that people can change their mind when presented with different perspectives. Oftentimes, being likeable (or at least respectable) is a prerequisite for getting someone to listen to you in the first place, so it's a central pillar to being influential.

Manipulation on the other hand, doesn't respect someone's autonomy. It might involve deception, threats, coercion, etc, but it ultimately aims to make someone do something that they don't want to do.

If you're getting a little kid to eat his dinner for instance, persuasion might appeal to his motivations (e.g. having more energy to run faster), while manipulation might look like saying not eating would make his mom sad (guilt tripping), or that he wouldn't get to play with his favorite toy (threat).