It is manipulation, you are doing things that impact how others view you in an effort to get them to do/feel/think something. Human interaction is various forms of manipulation.
Many people hear music and can put together some moves without thinking about it, others have to deconstruct, learn, and rebuild... it's still dancing either way.
Manipulation vs influence is about intent and degree of peoples ability to reject it.
If someone is influencing (actually) other folks can take it or leave it, and someone is willing to own it - because it’s something they actually believe.
Manipulation is non optional, and if rejected causes attacks of various forms because people are doing it not because they believe it/it will help the ‘target’, but because they are trying to extract something or control the target.
It’s the difference between ‘follow me if you’d like’ and ‘do what I want you to do or else’.