Blue Peter badge entry- help!

[bluepeterentry]

I am so confused- normally I turn up and pay full price adult entry to an attraction, show the blue Peter badge and dc get in for free.
I am having a bad day but can't work out the terms for where we're going next weekend- I've attached a screenshot below but what would your interpretation be?! Looking online suggests that e-tickets must be bought before midnight the night before...

I would say you buy on the day from the ticket office but they will issue you an eticket priced as if you had purchased online the night before (so not charged at on the gate price)

You need to buy your ticket in person in order to get the free child place. Any other people going with you should buy their tickets online, in advance.

That's what I thought but online says e-tickets can't be bought on the day. I contacted them and they just sent the info shown so maybe not just me who's confused 🫤