Living in Canada, I tend to notice a wide variability in the response times of ATMs to withdrawal requests (i.e. the time between when you finalize the transaction request, and when it spins up the bill spitter) and I think the one factor I've noticed it coming down to is the number of interchange networks marked as being supported on the side of the machine.
The ones that just do Interac (the Canadian interbank debit-transaction network) are quite quick; the ones that do Interac and PLUS or Cirrus are slower; the ones that add support for cash advances on plain credit cards by supporting individual CC companies (Visa, AMEX) are slowest of all.
So, maybe it's not the number of applications on the card, per se, but rather the number of applications supported by the terminal, with some sort of O(N^2) interaction between them?
Eg. TVR: 0000008000 (Byte 4 Bit 8) Transaction exceeds floor limit
Floor limit being the $/EUR/whatever amount that could be approved offline.
The 2 in the diagram appears to be pointing at a cleartext credit card number.
The difference is probably faster data connections and more efficient protocol implementations, I would think.
[0]: For some reason receipts here contain quite a lot of information on what happens behind the scenes if you know how to read it. I hope this link keeps working, it contains exercepts of receipts merchants give you here: http://docplayer.org/storage/33/16568026/1498495227/GbAKHYXN... With that information you can e.g. see which steps were perfomed offline.