Cloud clips are 30 second clips triggered by activity in view of the camera based on pre-determined rules. There are upload limits described here.
SVR is 24/7 recording stored locally. That is the main difference. The Alarm.com SVR is recording everything at all times for the cameras you choose to connect to it, not clips.
The SVR does not have upload limits, etc. The limits to how much it can record are entirely based on the size of the hard drive in it and how many cameras are connected.
Like, for example, if I have the SVR can I avoid paying a monthly fee?
No. The SVR is a service in addition to base video service and it costs more for SVR access. Alarm.com cloud video is a pre-requisite for using the SVR. We include SVR access in a couple plans. SVR support is available in the Complete and Protect plans (or the Cam plan if you want a video only Alarm.com account.)