The two exams are identical in every respect apart from some of the topics. The syllabus, level and format are the same. The Schools version focuses more on school life, and on the type of hobbies and interests which young teenagers are likely to have. The standard PET version, meanwhile, sometimes focuses on careers and independent travel, for example.
Basically, it doesn't matter which exam you take. In fact, the majority of candidates who take 'regular' PET aren't adults - most are in the 14 to 18 age bracket. So, if you are in your mid teens, you'll be fine taking the standard exam.