shooting for DEMs

Your image set is processed and a DSM** (Digital Surface Model) is generated from your images.  The processor uses the meta data from an image taken just before takeoff to somewhat calibrate the elevation of the set.  You can make the DSM much more accurate to the actual MSL elevation by adding some GCPs.

**a DEM or DTM usually have all non-bare-earth objects (vegetation and man-made objects) removed.

Terrain following in the app allows the craft to collect images while adjusting the flight path to try and maintain the same AGL for each image as best as practical.

So should I be flying a grid pattern instead of the back and forth pattern to get more more images?

The back and forth (lawn mower) pattern with good overlap is what you want.

https://support.dronesmadeeasy.com/hc/en-us/articles/207743803-Overlap-Management