The vim binary is able to answer by many names and it will tweak its behavior based on which name it is called.
This is a somewhat common practice in Unix, where a program will support checking the name by which it's invoked and will behave differently depending on that name.
At installation time, a single binary will be copied, but symbolic links or ...
To extend on accepted answer: you can just read exactly same number of bytes from both files:
vimdiff <(hexdump -C -n $(stat -c %s small) big) <(hexdump -C small)
On Mac OSX, the command will instead be:
vimdiff <(hexdump -C -n $(stat -f %z small) big) <(hexdump -C small)
By default vim -d (at least my version, 7.4) will open files in vertical mode, i.e. side by side. (This is equivalent to using -O option.)
To open files in "stacked" mode, i.e. one below another, add -o option.