Para responder à sua pergunta principal, não, eles não fazem a mesma coisa.
dd works on the file you specify, making it able to copy data between devices, or from a device to a file. This is commonly used for moving data if devices specifically are involved (create an iso image from a cd-rom disc for example: dd if=/dev/cdrom of=mycdrom.iso), or backup raw devices (sometimes used in RAC databases: dd if=/dev/raw/raw1 of=device_raw1)
cp is used for duplicating file content to a new file or to a new location. things you specifically want there are preservation of ownership, timestamp and mode (rights), and being able to recurse the operation (=being able to copy directories).