What is the difference between this is "لا توجد"
Is this just a more formal way, literally "X does not exist"?
la toojad is for a feminine object. la yoojad is for a masculine object.
*this and لا توجد
Yes, there is. We use ليس to form جملة اسمية which expresses the الثبات while لا توجد is to build جملة فعلية which has the التجدد expression. But, in English translation, I think the meanings would be the same.