A Directorate-General (abbr. DG) is an administrative branch dedicated to a specific field of expertise (e. g. agriculture). It is very similar to a ministry, but we can’t call them like that or Member State (abbr. MS) is how eurocrats call a country which is part of the European Union. Clear writing guidelines recommend using EU country or EU countries instead, but some habits are hard to die.... will be scared that the EU wants to take over their sovereignty.
The head of a DG is a Director-General (also abbreviated as DG, just to make things clearer). A DG is made of Directorates, a Directorate is made of Units, big Units are divided into Sectors.