On ESI.info a case study entry is written up in a structured way giving 3 sections for the entry write-up: the challenge / what you did / the outcome and benefits.
A project on the other hand has a looser format with the options to customise your own headers and create your own structure.
If you are unsure, we generally say write your entry up as a project as it's easier!
There is no difference between a Case Study and Project on live entries on ESI.info; this is only relevant to how you set the entry up in the Content Management System.
Watch this short video to see what the difference is when you set the entry up in the Content Management System.