North, northern, east, eastern etc
The words eastern, western, northern and southern are used to talk about rather indefinite areas. The words east, west, north and south are used to talk about more clearly defined places.
The eastern part of this country is barren. (NOT The east part of this country is barren.) (Here we are talking about less definite areas.)
The kitchen is in the east side of the house. (More natural than ‘The kitchen is in the eastern side of the house’)
In place names the words east, eastern etc are used with no difference in meaning. It is usually a matter of custom.
With some place names North, East etc are used.
With some place names northern, eastern etc are used.
The words east, west, south and north begin with capital letters when they are used in official place names.
The Middle East (NOT The middle east)
North America (NOT north America)
In other cases, we begin these words with small letters.
The sun rises in the east.
He came from the west.