Not sure where some of the other comments have come from as not really accurate.
Executive is an SC grade. You move to this grade after finishing the grad programme (about 3 years) or when you join as you are as an experienced hire. The grade can be quite broad but you def won't be managing workstreams. As you move to manager, you'll be looking to do this as part of your business case but you are expected to manage your workload which will then be reviewed by the manager. What Short Hair, Shiny Shoes is describing is how you need to perform before promotion to Manager.
The progression route in the other posts is correct. You go to Manager after Sc/Exec (usually 3 years) then to Snr Manager (depends on how good you are at sales - can be a very long time at SM), then Director. EY has introduced a split in the career path after Director. You can go to Partner where sales are the focus on you have equity in the firm, or to Exec Director which is a new grade and you are still salaried.
On the difference in Exec, this is a blow back from before Advisory. There was Bus Advisory Services (BAS) started about 5 years ago with lots of Accenture refugees and Business Risk Services, which had their Programme Advisory and TSRS service lines. PAS and BAS were merged to form Advisory and TSRS was merged with another service line to form ITA. The grades were all made consistent and we adopted the BAS terms of Consultant, SC, M, SM, D, P. I'm not sure why the ad still says Exec as this is called SC now.
There is no such thing as Senior Exec. The Consultant grade was called Associate.
Whether its Exec, Associate, etc, if its for Advisory in one of the service lines, this is consultancy role - client facing engagements. The internal back office support roles are different and not aligned to PI. Progression is as described above.
Hope this helps