What are E2 and E4 airspace?
According to this website, which directly quotes an internal memorandum of the FAA, the class E airspace can be categorized as below:


E1 – Class E Airspace at and above 14,500 feet MSL 
E2 – Class E
airspace areas designated as a surface area for an airport 
E3 – Class
E Airspace Areas Designated As An Extension To A Class C Surface Area
E4 – Class E Airspace Areas Designated as an Extension to a Class D
or Class E Surface Area 
E5 – Class E Airspace Areas Extending Upward
From 700 Feet Or More Above The Surface of The Earth 
E6 – En route
Domestic Airspace Areas 
E7 – Offshore Airspace Areas 
E8 – Class E
Airspace Areas Designated As Federal Airways


The memorandum is also available as PDF. 

Apart from this reference to the FAA internal memo, I could not find any official FAA documents explaining the categories. 

For pilots and controllers there seems to be not many differences, but for operators of small unmanned aircraft (i.e. drones) there are.