When you put it like that it's really stark.
Could it be that the 103k is higher because close contacts are being identified and told to get tested and more of those are coming back positive? With those close contacts coming back positive it's similarly reducing the numbers in the 'just isolating' category.
Previously when a whole bubble was told to isolate because of a positive test I expect many of the close contacts wouldn't have gone for a test unless they showed some symptoms.
There isn't really a just isolating category though. Kids under 18 still attend school even if they are a close contact, they only isolate if specifically asked to by NHS test and trace. They continue to attend even then until the result of the PCR.
There are two particular parts of the school guidance that lead to the changes between July and now:
"NHS Test and Trace will work with the positive case and/or their parent to identify close contacts. Contacts from a school setting will only be traced by NHS Test and Trace where the positive case and/or their parent specifically identifies the individual as being a close contact. This is likely to be a small number of individuals..."
"Individuals are not required to self-isolate if they live in the same household as someone with COVID-19, or are a close contact of someone with COVID-19, and they are below the age of 18 years and 6 months"
These are big changes, imagine two scenarios: First that my son tests positive - I have absolutely no idea who he interacts with on a daily basis in school but I'm supposed to identify the close contacts? Second, that my wife tests positive - my work have requested that I stay at home regardless of the government guidelines, but my son is supposed to continue going to school. The only thing that changes that is when (if?) test and trace contact my wife to identify close contacts and if they then decide my son was one.
In scenario 2, I'd be keeping my son at home, but technically I can be fined for doing so if I gave that as the reason, he's supposed to go to school.
I would imagine from the numbers above, that the 16k are actually school kids that have been identified by NHS test and trace due to a parent testing positive, not from a classmate testing positive.