You are correct. Service mode is like safe mode in the Windows world, with a twist. Depending on your flavor (distribution), service mode can mean a few different things. For the most part, it is usually runlevel 1. That means that when the machine is turned on, it will load a bare minimum system and leave you at a root console. That means no gui (graphical user interface).
More recently, distributions have been adding a "rescue" or "service" mode to the boot options that allows you to boot to a gui in what is similar to Windows "safe mode", however, does not offer the flexibility of a system in runlevel 1.
You can google runlevel 1 to learn a little more about it. I am going to recommend that you stay away from this until you know a little more about it. A single typo can leave you with a "busted" system that is unbootable.