>The download of SQL Server 2012 SP1 is quite big. It is 3.63 GB for the 64-bit version. Is this a full version of that is really the update?

It's full SQL Server with SP1. The update is at the bottom and has size of 929.2 MB

"Microsoft SQL Server 2012 SP1 Update - this package contains the Microsoft SQL Server 2012 Service Pack 1 update to be applied to existing SQL Server 2012 installations.

Microsoft SQL Server 2012 SP1 Slipstream- This package provides the capability to perform new SQL Server 2012 instance installations (or SQL Server 2008/SQL Server 2008 R2 Upgrades) culminating with Service Pack 1 pre-installed. "