Classical recessions were often caused by shocks that reduced the natural rate of interest. As market interest rates fell (there was no Fed), the demand for gold increased. Because gold was the medium of account, this was a negative demand shock.
Modern recessions occurred because the Fed struggled to control inflation, as we gradually moved to a fiat money system after the Depression. Inflation would rise too high, and this would cause the Fed to tighten.
I recall that Paul Krugman once did a post suggesting that the most recent recessions were not caused by the Fed, but rather were caused by factors such as bubbles and investment/financial instability. The recessions of 1991, and especially 2001 and 2008, were not preceded by particularly high inflation expectations, which were well anchored by Taylor Rule-type policies. Thus, these recent recessions (in his view) were not triggered by tight money policies aimed at reducing inflation, as had been the case in 1982, 1980, 1974, 1970, etc.
I suspect that the post-modern recessions are indeed a bit different, but not quite in the way that Krugman suggests. Although I don't think interest rates are a useful way of thinking about monetary policy, I'll use them in this post. (If I just talked about slowdowns in NGDP growth it would not convince any Keynesians.)
In the New Keynesian model, a tight money policy occurs when the Fed's target rate is set above the natural rate of interest. In 1981, that meant the Fed had to raise its interest rate target sharply, to make sure that nominal interest rates rose well above the already high inflation expectations, high enough to sharply reduce aggregate demand. In contrast, interest rates were cut in 2007, despite a strong economy and low unemployment. The natural interest rate started falling in 2007 as the real estate sector contracted.
In a deeper sense, however, the postmodern recessions are no different than pre-1990 recessions. They still involve the Fed setting its fed funds target above the natural rate. The difference is that in recent recessions this has occurred via a fall in the natural rate of interest, whereas in 1981, it occurred through a sharp rise in the market rate of interest.
You might say that we used to have errors of commission, whereas now we have errors of omission. But that only makes sense if you accept the notion that interest rates represent monetary policy. But they don't. Every major macro school of thought suggests that something other than interest rates represent the stance of monetary policy. Monetarists cite M2, Mundell might cite exchange rates, New Keynesians cite the spread between market rates and the natural rate. No competent economist believes that market interest rates represent the stance of monetary policy.
Thus, in the end, Krugman's distinction doesn't really make any sense. It's always the same - recessions are triggered by the Fed setting market interest rates above the natural interest rate. Since 1982, the natural rate of interest (real and nominal) has been trending downwards. This was an unexpected event that very few people forecast. (I certainly did not.)
The Fed would occasionally end up behind the curve in terms of noticing the decline in the natural rate. The FOMC would only realize its error when NGDP growth fell well below their desired rate. Then they'd try to ease policy, but initially, they'd underestimate how much they needed to cut rates in order to get the proper amount of stimulus. The natural rate was lower than they assumed. Hence slow recoveries.
My hunch is that we are coming to the end of this long downtrend in the natural rate of interest. That means that future recessions will be caused by some other type of cognitive error. That's also why I expect this to be the longest economic expansion in US history. But that's not very impressive when you have such a weak recovery. Much more impressive would be the longest consecutive streak of boom years. Now that would Make America Great Again!