There is a good article by Lyn Alden on this, but basically, the difference is how the QE is targeted. In 2008, the QE was done in order to get rid of toxic assets and recapitalize the banks - most of that money stayed locked up in the financial system and never made it out (banks had reserve requirements changed and tightened credit, which shrank the money supply - the QE was done to counteract that).
This time around, the banks are well capitalized and the QE is targeted at monetizing the federal deficit (federal government issuing treasuries in order to finance relief packages and the like and FED buying them), so the money is actually going to make it into the broad money supply, which might lead to inflation (though hyper-inflation is probably an overstatement at this point).
Basically Lyn compares what happened in 2008-2009 to 1929 - which was a banking crisis; whereas what happened in 2020 is closer to 1940-1945 / late 1960's in terms of the FED monetizing the debt. We had inflation in the late 1940's and in the 1970s, so it's possible we'll see something similar.