An external HDD (or Hard Disk Drive) is pretty much the same as the HDD inside your PC. It still has a magnetic disk that rotates at high speed, and it still has a reader that is incredibly delicate. The difference is that you can easily disconnect it from your PC and stow it safely.
An SSD (or Solid-State Drive) is the more modern and robust equivalent. Unlike an HDD, it doesn't have any moving parts, and it's much quicker when it comes to reading and writing data. The downside is, SSDs are still significantly more expensive than HDDs, though it must be said that over the last few years, the price has gone down, and it will probably continue to do so.
On balance, an external HDD should work for most users, and if the volume of data you need to back up is not that huge, an SSD is a sound investment.
If your website's total content is not more than a few GBs then it is good to go for SSD storage.
If you have more content but can go for limited speed then you may use HDD.
For instance, If you are going to blog then I would recommend SSD.
But if you are going to be setting up an e-shop then HDD is the way to go.