There is a difference in intimacy and intensity.
Often those who are emotionally intense also had childhoods where they had to please the adults around them, and weren’t allowed to be themselves. This meeting of other’s needs carries into adulthood, making intimacy hard.
Intimacy shows that you are fully yourself around someone, even as you accept them as they are and create an environment they can be fully themselves. Key words here are acceptance, authenticity, and trust