I need advice on how to handle this situation that happened with my dog and the neighbors dog

My dog and the neighbors dog, both male German shepherds, (mine is 6, theirs is 10) are normally great friends and get along so well. They play nicely and are very cute together, normally off leash while we’re on a hiking trail behind both of our homes, and sometimes in each others yards.

This morning though my dog was on a leash and the neighbors dog was off the leash, and my dog attacked their dog. Both dogs are fine — no blood, no broken skin, no hurt bones. But my dog had his dog on the ground, neck in his mouth, they were growling.

I pulled my dog away as fast as I could, but it happened so fast. It probably was under 10 seconds from start to finish, and they were wagging their tails after.

I apologized profusely to the neighbor, asked if their dog was okay and just was so so so upset for them. And embarrassed and ashamed!! We talked for about 5 mins after the fact and she said it was okay and she understood how German shepherds can be. She told me she thought it was because my dog was on a leash so he felt restrained? Idk.

What else can I do to apologize? I feel awful…ugh. I’m so grateful for her understanding but I want to do something more.

Thank you.