Generally you will use the File > Save to save your work with full
information as a
.aseprite file (both are the same, just
the extension is different). Then you can export your sprite to be
used in other programs (a website, videogame, etc.) using File > Save
Copy As to export your sprite to
.gif files or a sequence of
files. See the Save menu section for more information.
You can see the File > Save Copy As as an export/or publish option, which will remember the latest options you've used in case that you want to save the copy again.