An economic depression is a form of a recession. A recession is determined as two or more consecutive quarters of negative GDP growth; while a depression would be measured in years and not quarters.
In the Great Recession, the United States experienced 6 quarters of negative GDP growth (3rd quarter 2008 to 1st quarter 2010) so it was more than a simple recession but it did not quite meet the standard for a “depression” as we were only in a recession for about a year and half.
Had they been in official recession for say 8 quarters or more (there are four quarters in a year), a conversation could have been had whether it was a depression instead of just a recession.
Some argue that they were in a depression; however, the stigma associated with the Great Depression provides that the term is only used as a last resort. No government wants to admit they are in a depression as that word is automatically associated with the hardship of the early 30s.