A Casual Affair's Intensity

I'm in my early 50s and a college professor. For the past few months, I've been casually dating this woman who is also a colleague, about ten years younger than me. We met at a conference last year and hit it off immediately, both of us divorced with kids grown up, no real ties holding us back from enjoying each other in the moment. Anyway, we were on vacation together this past weekend at a remote cabin far from campus or prying eyes, and I had her pinned against the wall in our cozy rental. Her dress hiked high above her thighs as my hands gripped firmly into her hips. She was arching back to give me better access, her body moving sinuously against mine. There wasn't much time for gentle foreplay, we just needed each other too badly. Once I had her on the bed, I couldn't wait any longer and entered her in one thrust, feeling her warmth grip my length as if she was pulling me inside her very soul. We both moaned loudly, our breaths coming out in sharp gasps. Her legs wrapped around my waist as I moved within her, her nails scratching at my back. I felt a wave of intensity building up, that edge where pleasure and pain become one, and it just took everything to the next level, she was gripping me so tight, my own climax was right there at the surface too. We both screamed out as we reached our peaks, her inner muscles clenching around me again and again. Afterwards, lying tangled up with each other, I couldn't help but wonder if this is how things should be, or if it's just because we're free to indulge without ties holding us back. Have others felt the same intensity when dating casually? Is this what people talk about as 'lovers' versus 'partners'? It was so much more raw and unfiltered than anything I've experienced in a long-term relationship, but also feels fleeting, should that concern me or is it just part of enjoying being single again?