See the manual page for apt-get.
Download only; package files are only retrieved, not unpacked or installed.
The 2 options are the same and do identical actions. So you can use either one.
In general: most times options come in 2 forms: short and long. From apt-get you can also use -f, --fix-broken or -m, --ignore-missing, --fix-missing or -q, --quiet. All of these groups mean the same and will do the same.
Some people prefer long options. Some prefer short options. In software languages (like Python) you have a method where you can split option + value into an array. And it then also will have a method to define sets of options for short and long version. So it is possible to satisfy everyone's need for options :)
apt-get download was added in version 0.8.11 of apt as another form of
-d where the download is done to the current directory.