Both the File | Export command and the Map Tools | Layer Tools | Export Contours command export to DXF, SHP and text files (DAT, TXT, etc.). 

• Map Tools | Layer Tools | Export Contours
  This command will export only the contour lines. One benefit to exporting the contours in this way is that you don't have to turn off extra layers, axes, or other objects. This command is useful if you want a 3D SHP file, where each vertex in the SHP has a Z value associated with it (instead of a single Z value for each line feature).
  
  
• File | Export
  This command will export all objects (or all selected objects) in a plot window. It is useful if you want a file containing text labels, line colors, or other objects in addition to the Z value. For example, to export a color-filled contour map to a SHP file (or a 3D DXF) with Z values saved to the DBF for each contour polyline, use File | Export.
  
  

Related articles:

• How can I export a 3D DXF file from Surfer containing the X, Y, and Z coordinates of my contour lines?
• How can I export a contour map from Surfer to a 3D DXF file and display it in AutoCAD in 3D?
• Can you give me some examples of the SHP files exported from Surfer?
• How can I export contours to an XYZ data file from Surfer?

Updated September 1, 2020