Yeah, seems like the nature preserve portion seems to be called Allerton Natural Area. Making that a separate area seems reasonable. The wikipedia page and this book (https://www.google.com/books/edition/Inside_Allerton/uZziAQAACAAJ?hl=es) call it Robert Allerton Park. Perhaps the Park & Retreat center just refers to the central area and Robert Allerton Park refers to the whole area. Or maybe they updated the name. 