Just to clear away any confusion on the subject, the newspaper definition of a recession is a period of economic retraction. It's when the economy actually gets smaller. Usually, two months with declining GDP, or Gross Domestic Product*, or a severe rise in the unemployment rate are warning signs that the country is nearing, or in, an economic contraction.
Now, this may sound like a depression, but there are differences. The reason the two are hard to distinguish is because there is not a universally agreed upon definition. The more economists one asks, the more answers one is bound to receive. That also is why some sources say the US is in a recession, and why some say the US is not in a recession. A generally agreed on rule would be as follows:
A depression is when the GDP falls more than 10%, while a recession is not as severe.
Not quite fool proof, but it is a mostly accurate generality.
*Gross Domestic Product is the total market value of all goods and services produced in a country in a given year.