I'm one of those people-For clarity I'm referring to influence in the active 'How to Win Friends and Influence People' sense. To me "influence" and "manipulation" seem like forms of persuasion but with positive and negative connotations, like "public relations" versus "propaganda".

None of them are necessarily bad on their own, but the choice of words seems like it depends on the perspective who is perceiving or describing the influencer/manipulator and their motives. Influence can be seen as manipulation and manipulation seen as influence.

For example someone who dislikes an "ifluencer" is probably more likely to think of them as manipulating their audience into buying products. Convincing someone to join a religious group could be seen as positive influence by current members, and manipulation by an outsider.

Clarity of purpose from the person doing the persuading is not necessarily clear as well. There is likely there's likely a mixture of factors motivating them to persuade, including some to their own benefit. People, especially those who think they are doing good, will also generally grade themselves on a bit of a curve and rationalize their actions towards being positive, especially in moral and emotional contexts.