A surface is an image of a specific size with the pattern repeated on it.
With tile export, you need to rebuild the repeating pattern in other software. With a surface, you get the repeated pattern ready to go, at any size and repeat count.
Many software applications will repeat a pattern from the top-left corner, which doesn't look so pleasing. By default, Repper will centre the pattern, creating a more balanced image.
When the horizontal or vertical repeat count of a surface isn't a whole, the surface itself cannot be repeated anymore. If you want to surface to be repeatable itself, unlock the repeat count and set both values to a whole number (no decimals), as described here.
Building a surface takes more time than a single tile. If you are exporting very large bitmap surfaces, it may take minutes for a single surface. Vector surfaces can take even longer, all depending on the amount of detail and repeats (see some tips here to avoid long export times for vector).
Obviously, a surface will take up more storage space than a single tile. If you are exporting a pattern to be used later and you know how to repeat the pattern in other software, exporting as a tile is the most versatile and compact way to save your pattern.
You find the tile export by selecting the Export tab (1) and then choosing the Surface tab (2a): or select Surface from the Dropdown menu
(2b):