If parents can eat with you on your birthday, it’s probably elementary school, and the kids probably typically sit with their class. If a parent shows up for a birthday lunch, they probably sit them at a separate 4-top from the whole class, so they can pick 2 other students to sit with the kid and their parent.
In my kids elementary school, we just sat at the long table with the whole class, but I could imagine that scenario if the kid/parent sat at a different table. If you didn’t specify a couple of kids and left it as a free-for-all, there would be chaos.