My understanding, going by the eConnect install/admin guide is this:
>> 'eConnect Service User' window
To access the eConnect business objects, the eConnect Runtime Services
requires a user login and password. In addition, the Incoming Service, and
Outgoing Service will use this account. Enter the domain\login and password
credentials for the user account you set up as an eConnect prerequisite.
The account must be a member of the DYNGRP role in the Microsoft Dynamics GP
system and company databases on your Microsoft Dynamics GP SQL Server.
>>'SQL Connection Information' window
Enter the name of your Microsoft Dynamics GP SQL Server. Also enter the
name of the Dynamics GP system database.
Click the type of authentication you want to use. Typically, you can use
Windows Trusted Authentication to connect to your Microsoft Dynamics GP
SQL Server. If your Windows logon account cannot access the Microsoft
Dynamics GP server, use SQL Authentication and specify a SQL user name and
password. Click Next to continue.
You can prevent the install from creating a connection to a SQL Server. If you mark
the Do not add service user to SQL box, the SQL connection is not created. You
might want to click this box when you do not know the SQL Server or the Dynamics
GP system database that you want eConnect to use. For example, you install eConnect in a multitenant environment and you do not know the name of the system database for your tenant.
So, it looks like the 'SQL Connection' information is used to make the connection to the SQL Server during the installation of eConnect, while the 'eConnect Service User' is used to access the eConnect objects and run the service.
The DYNGRP database role gives this account the EXECUTE permissions on the stored procedures which are what eConnect primarily uses, along with SELECT, UPDATE, DELETE and INSERT permissions on GP tables.
Hope this helps, as I agree, it isn't the clearest information.
Thanks