You're actually right. It's just the uncontrolled non-suppression of the first wave. It didn't go anywhere, despite people walking around acting like it wasn't real and childishly calling anyone who said it could come back a 'dementor'.
So what defines a 'second wave' if this is not it then? Lots of people made the most of the summer, went out and tried to enjoy themselves as much as is reasonable during the season where viruses and other bugs are at their lowest and schools were off, and I bet they are bloody glad they did now, because this rise in infections was inevitable unless we stayed locked down completely until a vaccine, and we are now entering flu season as well and it's going to be shit winter!