Breaklines and faults are used differently in Surfer. To visualize how Surfer uses each of these, we'll be using the below grid displayed as a contour map. The Surfer SRF project file and the BLN file used for the faults and breaklines are attached to this article. A BLN file is a Golden Software proprietary text file that is required to apply a fault or breakline to a grid.

Original contour map without faults or breaklines.

The same data set gridded with two 
faults and displayed as a contour map.

Faults occur when there are differences in Z values on either side of the line. This could be because of a geologic fault or another reason, such as a landslide or a building. Faults only have X and Y values in the BLN file. When gridding, Surfer sees the fault as a stop. It cannot look through the fault to the other side for data.  It can go around the fault, but the distance will increase and the data on the other side of the fault will have less of an effect on the grid nodes. If the fault is a polygon, and all data points are on the inside of the fault polygon, then the area outside the polygon in the grid file will be assigned NoData values. There is not a way to specify direction of movement or amount of displacement along a fault in Surfer, as they aren't specifically geological faults.

 
The same data set gridded with
two breaklines and displayed
as a contour map

Updated October 2021