Your two main options for external drives are a traditional spinning platter hard drive (HDD), and solid state drive (SSD). Your SSD is more akin to a standard USB stick where you're storing all the data in little flash memory chips rather than writing it onto a metal platter. That makes them more robust, but also more expensive and lower capacity.
Hard drives are still valuable in that they can provide cheap, seriously large volumes of data storage. And if you don't need to access that data quickly or regularly they're just fine. Transfer speeds of hard drives really are a fraction of what you'll get from a quality SSD.
An SSD, however, is far quicker and generally smaller, which makes them more portable. Their speed means that they're far better suited to being an extension of your game library in that you can actually play directly from the SSD itself.