CIC has made changes to the ECAS flowcharts as late as June 2015. I distinctly remember that there was a stage called In Progress earlier on this flowchart but that has disappeared now. I believe that this is the transition time from the old process to EE and there isn't a lot of clarity in ECAS flowchart but the broad status transition appears to be In Progress > Application Received > In Process > Decision Made.
Of the following 3 flowcharts, the 3rd one appears to closely approximate ECAS status under EE. It isn't a complete match clearly because Medicals happen earlier in the new process.
https://services3.cic.gc.ca/ecas/redir.do?redir=app_perm_fam&lang=en&app=ecas --- Outside Canada
https://services3.cic.gc.ca/ecas/redir.do?redir=app_perm_com&lang=en&app=ecas --- Inside Canada
https://services3.cic.gc.ca/ecas/redir.do?redir=app_perm_wrkr&lang=en&app=ecas --- FSW to CIO, Nova Scotia
If you observe the flowchart in the 3rd link, Application Received implies that
"We have received your application. After checking for completeness, a file has been created and the information from the application form was entered." and In Process implies that
"Based on review of your complete application package, it has been determined that your application is eligible for processing. Processing has begun."
What that possibly means is that when ECAS status is In Process, your application is deemed complete AND eligible under the particular program. Of course, there could be exceptional misses like anvar21 where the rejection most likely happened because of program ineligibility and one would expect that CIC would catch that miss upfront rather than wait for such a long time before rejecting the application. But the system is as new to them as it is to the rest of us so such errors might creep in for now and the system will be fine-tuned as we move along.