A periodic curve is a smooth closed curve. Periodic curves stay smooth when you edit them.
A non-periodic curve is a closed curve with a kink at the start/end of the curve. Deforming non-periodic curves near the start of the curve may result in kinks.
Periodic surfaces are closed surfaces (such as a cylindrical surface) that can be deformed without developing kinks. Periodic surfaces are automatically created when the input curves are periodic.
A non-periodic surface is a closed surface with a kink at the start/end of the surface. Deforming non-periodic surfaces near the start of the surface may result in kinks. Non-periodic surfaces are automatically created when the input curves are non-periodic.