Open nib - traditional pen design, where the whole nib is exposed - often attractively decorated.  The nib can feel slightly more flexible but it can dry up quicker if the cap is left off for a minute and it is easier to get ink on your fingers.

Hooded nib - only the tip of the nib is exposed, the rest being inside a plastic "nib shell".  More resistant to drying up, less easy to get ink on your fingers but arguably less attractive.

Hooded nibs make it possible to hold the pen closer to the tip, which can suit some people.

Both types of nib can be equally good, smooth writers.

There are other nib designs, such as the Sheaffer "inset" nibs used on the Imperials and the PFM.  Most of these are best regarded as a variation on an open nib.