Intimacy vs Sex- Are they one and the same?

This weekend I attended a gathering at the home of my friend, who happens to be one of my yoga teachers. The evening was a celebration of the Equinox, a time when the balance between the light and dark is struck. The intended schedule of the evening was to have a brief yoga flow, a shared dharma talk and contemplation followed by silent meditation, some sound healing and perhaps time to dance and play on her trapezes and lyra aerials.
What happened instead was a bit more free form and unorganized. Not all of the attendees were on time for when she wanted to have the yoga, and most of us paired off or made small groups to talk. While we did get to the dharma talk, meditation, sound healing and play time, the official yoga period was replaced by socializing and enjoying really delicious and nutritious food.
I can be a little shy in social situations, particularly vanilla ones. When I am wearing the Domme mantle at play parties or events, though it has been years since I have been to one, it is easier to find my footing. Being that my work is deeply sexual, I often feel the need to sanitize what I actually do for a living. Such is life amongst the normies.
However, on this evening I had decided to really embody the Sutra of satya, truthfulness. I have been feeling like it is beyond overdue for me to share the essence of the life work that feels like a calling to those who wish to know me. A lifetime of being shamed can do a number on the ability to speak one's truth. I no longer wish to wear manacles I never consented to put on. I am proud of who I am and what I do, and I need to start speaking on it, regardless of whether or not people are discomfited by it.
As the scattering of individuals would have it, I found myself seated with a woman in her late 40's and a man in his 60's. Him I know from taking hot hatha and contrast therapy plunges together, but her I knew not at all. They asked me what I do and I said the usual reductive answer of sex coach and well, that usually unleashes the torrent of questions. I explain that I use kink protocols to help people achieve mental and physical wellness, but the bulk of my work is with men 30 and under who are struggling to relate to humans after prolonged porn consumption and speaking only to AI. I explained that I help people internalize their desires and inhabit their body when aroused. Following this, I spoke of how the male loneliness epidemic isn't the meme people think it is. Real people, men and women are in pain and seeking connection. I teach people how to love themselves as a foundation before seeking love from another, to gain access to their sexual agency through masturbation and beyond that help them explore their kinks and desires, become confident in them, and then develop a language to express them. I mentioned how I teach people how to cultivate intimacy with someone, before it ever gets into the realm of sexual desire.

The pair were on board with my words until this point. The woman who at first had said she would love to engage my services due to putting up walls after her divorce was gobsmacked and said, "Well, sex and intimacy are the same thing!" The gentleman agreed. At this it was my turn to be rocked back on my heels a bit. In my purview the two are VERY separate entities. For a moment I thought the distinction was perhaps my own after years of being a sex worker. Clearly I have had lots of sex play that was not at all intimate, and usually geared towards their tastes not mine. I tried to explain why I made the distinction. Sex can be very intimate, and the connection between parties profound, or it can be a far more casual affair. Certainly I also have intimacy with people who I am not spending time naked with. Well, not physically naked, but with a very bare soul instead.

I have been ruminating on the lack of separation of the two things in the minds of my conversation companions. Surely, this woman and I had achieved a level of intimacy that night. At one point, she expressed she missed physical touch so I embraced her in a long hug, little space between us. I rubbed her back and told her she was worthy of attention and love and the walls were just alienating her from her own desires. She buried her face in my neck, wiggling her bum and sighing. She said she wished she could be like the cat at the party and be as forward in asking for touch as the kitty who bumped her head against the hands of party goers was as she solicited a pat. I told her she could be as the kitty, with me. She squeezed me tighter. I felt the hunger in her, felt compassion for her longing. Surely, this is intimacy without sex. In her I saw what she longed for, and in the capacity I was able to, met her where she was at. Asking for nothing, I gave her my love and when we ended the embrace after a good few minutes, we parted and she glowed. Her demeanor was far different now, and she popped a piece of chocolate into her mouth saying, "candy and a hug like that, my night is now amazing." I gave her a smile and went to get a glass of seltzer.

I watched her for a bit out of the corner of my eye. She had been somewhat reticent and shy when she first arrived, and was now...flouncing. Her energy was buoyant, and her demeanor coquettish. She approached the sole young man present and flirted. It was fucking adorable as hell. "What a good girl", I thought.

In the days hence I have still been contemplating who and what kind of individual sees sex and intimacy as the same entity. I have never heard the two things united in my ENM or kink spaces. Is it the monogamous or vanilla who think it the same? Is it those who don't claim their sexual agency? I have no answers, only more questions. My meditation teacher often says, "the more I learn, the less I know". Well, that pretty much sums me up right about now.