When another child had a frightening experience, how should I explain it to their parent?

First, frankly offer an apology to the other child and parent for what happened, check for any injury, and show you care. Then, taking care not to make it an excuse, explaining concretely "this tends to happen in situations like this" and "here's how we're handling it now" helps the other side gain a clearer picture. Whether to share the diagnosis name depends on the situation; even without it, you can share what's difficult and the measures at home and preschool. Deciding on prevention (an adult stepping in, etc.) with the preschool/school and sharing it with the other parent as reassurance is constructive.