Hi,
Back to your original question: both of them take part in the start of sap system.
You can have a better overview about sapcontrol and startsap script here:
SAP Start Service - Architecture of the SAP NetWeaver Application Server - SAP Library
The sapcontrol webservice interface implements a wide variety of of other functions, e,g,
as here already mentioned GetProcessList but GetVersionInfo, ... GetEnvironment, GetStartProfile...
You can see here more detailed infos about sapcontrol web service functions:
Regards, Gabriella Kiss