Off the top of my head I can't give you a textbook definition of what a second wave might be. I'm not sure if we've ever had a second wave of this kind before. The second wave of the Spanish Flu was a mutation, whereas a second wave of COVID-19 would be the same strain, coming back because it now has access to a population who weren't susceptible due to lockdown.
The effective reproduction number (R) once we're in lockdown is estimated to be about 1.2, so the number of new cases will fall considerably the longer we're in lockdown, but as soon as you release lockdown, R rises again and cases will grow and grow.
So this is unlikely to be the second wave as numbers of new cases haven't fallen at all, or certainly not for any sort of prolonged period. We won't know for certain for a long time though.