> In the United States, it is defined as "a significant decline in economic activity spread across the market, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales". In the United Kingdom, it is defined as a negative economic growth for two consecutive quarters.
So it's not a recession unless it lasts for a while. So when the markets suddenly go down, it's not known if a recession is happening, until it's been ongoing. Since we've already been in lockdown for more of Q2 than Q1, its reasonable to expect that we're in a recession. But it's not official yet.
The NBER Business Cycle Dating committee explains their criteria and explains why "the two quarter rule" the financial press always talks about is not what they use.
https://www.nber.org/cycles/recessions.html
"The committee's procedure for identifying turning points differs from the two-quarter rule in a number of ways. First, we do not identify economic activity solely with real GDP and real GDI, but use a range of other indicators as well. Second, we place considerable emphasis on monthly indicators in arriving at a monthly chronology. Third, we consider the depth of the decline in economic activity. Recall that our definition includes the phrase, "a significant decline in activity." Fourth, in examining the behavior of domestic production, we consider not only the conventional product-side GDP estimates, but also the conceptually equivalent income-side GDI estimates. The differences between these two sets of estimates were particularly evident in the recessions of 2001 and 2007-2009."
The NBER definition is what gets used in the US by every single government department and academic.
The GDP approach is a lot more concrete. The NBER's approach is more nuanced due to evaluating more factors, but is also more hand-wavy.