A:AnswerShort Answer: An SSD is a type of Hard Drive and a portable hard drive is one of many ways to connect a hard drive.
Detailed answer: A portable hard drive is simply an external hard drive that is powered through the USB cable that you use to connect to your computer. A portable hard drive typically uses a standard Laptop hard drive for storage. These hard drives are smaller than the ones you'll find in desktop computers and are typically slower. They don't usually require an external power supply and are powered off of the USB connection to your computer.
A Solid State Drive is the newest form of Hard Disks for computers. SSD hard drives use the same type of memory you'd find in your typical usb flash drive except much faster. Most hard drives still use a rapidly-spinning platter to store data but with an SSD there are no moving pars so they are able to read and write data magnitudes faster.