What four directions which are not described by 四处 are described by 八方? I have a hunch about the difference between 八方 and 四处.
四处 includes north, south, west and east. 八方 includes these four + up, down, forward, backward.
Three questions:

Is my assumption correct?
Do native speakers really differenciate between these two phrases or they use them interchangibly?
Is there a reason why 八 is connected with 方 and not with 处? Is there a difference in the sense of &quot;direction&quot; given by 方 and 处?
四方 / 四处
现代汉语大词典

东南西北四个方向


四处 (or 四方) = north, south, east and west


八方
古汉语大词典

四方(东、南、西、北)四隅(东南、东北、西南、西北)的总称。


八方 = (north, south, east and west) + southeast,  northeast, southwest and northwest


四方 and 四处 can be used interchangeably. There is also a third one: 四面.
Another word you might want to know:

十面 = ((north, south, east and west) + southeast,  northeast, southwest and northwest) + up and down.

八处 doesn't seem to be a thing, but 八面 does exist.