What is different between the EV3 Home and Educational sets?
Both sets include an EV3 intelligent brick.

Hardware

The Retail (Home) edition (set 31313) includes:


2 large motors, 1 small
1 touch, 1 color, 1 infrared proximity , 1 remote IR beacon




The Education set includes:


2 large motors, 1 small
2 touch, 1 color, 1 Ultrasonic with red LED, 1 Gyro
1 rechargeable battery (battery charger sold separately)




Software

The software for the education version is sold separately to the core set. As well as the programming software, includes datalogging tools, and a firmware version that allows on-brick datalogging.  

There is also a difference regarding sensor support: only the education version provide blocks to manage ultrasonic and gyro sensors included in that version. NXT temperature sensor and Energy meter are supported too. And of course, models being different between edu and retail versions, the building instructions that are included in the software are different.

Robots

Each edition includes different Technic bricks and instructions for different robots. You can find a list of those robots at the LEGO Mindstorms EV3 Comparison project, and product pictures on Robot Square.

Parts

The EV3 Expansion Set adds many Technic bricks for even more robots and is suitable as an upgrade for both sets. However, to build all robots officially published by LEGO for either set you need to buy additional parts in any case.

The LEGO Mindstorms EV3 Comparison project on GitHub lists all parts in a spread sheet, tells you which pieces are missing from "education + expansion" to "retail + expansion" and vice-versa, so you can find out which parts (numbers + names) to order in addition.