There is a difference, and I recommend the typology presented by Lindsay (2015) be used.
Lindsay (2015) presents a typology which defines a pit as a single cell in a DEM whose elevation is below that of the surrounding cells and a depression as a region of cells which drain inwards to a pit. This is consistent with the definitions used by O'Callaghan and Mark (1984) in one of the earliest papers applying algorithmic approaches to digital elevation models: "a pit is defined as a point none of whose neighbors have lower elevations" and "the 'overflow' point was defined as the point which was on the boundary of the basin and which had the minimum elevation difference to the pit."
To establish the relative frequency of terms, I performed a quick literature search.
The term "depression" is used in the above sense by Jenson and Domingue (1988), Martz and Garbrecht (1999), Planchon and Darboux (2001), Jones (2002), Otto and Thurnherr (2007), Yong-He et al. (2009).
The words "pit" and "depression" appear to be used interchangeably by Jenson and Trautwein (1987), Ehlschlaeger (1989), and Grimaldi (2007).
The word "minima" has also been used to mean both depressions and pits by Vincent and Soille (1991) and Soille and Gratin (1994). The word ``sinks" has been used to mean both depressions and pits by Olivera et al (2000) as well as the ESRI corporation in various ArcGIS guides.
A minority of authors used only the word pit: Tarboton et al (1991) and Soille (2004).