As a user of an iPod (or any other device), you won't notice a difference at all. It's just a technicality that you don't really need to know about.
It'll make zero difference to your use of iTunes or the iPod itself.
As above, a hard drive is a mechanical thing. As such, walking with it is fine, but lots of running with it could introduce problems (imagine running with a record player -- the stylus would skip!).
A flash drive has no moving parts. So it's great for running.
Due to current prices and technology, hard drives are far cheaper and can store many more songs. Flash drives are newer and so are far more expensive, storing far fewer songs.
Many still jog with their hard drive iPods, without issues though. It's just that issues are more likely, especially with a lot of it. There isn't a problem with flash drives.
The only thing important to you is the storage amount -- 8GB, 4 GB, 80GB, etc. The higher this number, the more songs you can store.
As a guideline, I have 563 songs on my iPhone, taking up 2.3GB of space. So 4GB will give you about 1000 songs, etc.