Hi,
What are the key differences and when to use which: NurbsCurve vs BezierCurve?
https://developer.rhino3d.com/api/rhinocommon/rhino.geometry.nurbscurve
https://developer.rhino3d.com/api/rhinocommon/rhino.geometry.beziercurve
Also I see similar implementations for NurbsSurface and BezierSurface.
Nurbs are an extension of Beziers.
Beziers, depending on the implementation, can be rational or not (=have a weight). But they don’t have a concept of spans, knots etc..
A Nurbs curve essentially gives the ability to create a curve out of multiple Bezier curve segments.
Technically this means that a single-span Nurbs curve is equal to a Bezier curve. But of course, if you know you don’t need multiple spans, it is inefficient to store knots in memory and going through the same computational process.
However, if you use a Nurbs-oriented API like Rhinocommon, you still the need the NurbsCurve datatype to access the respective functionality.
Thanks.
Does it mean NurbsCurve inherits BezierCurve?
Or can a BezierCurve be represnted by a NurbsCurve because of a more complex implementation?
Do you know real life 3D modelling example when you use one over the other?
No there is no inheritance in Rhino. I don’t know the use-case for BezierCurve in Rhino.
I worked in exterior design in the automotive industry, primarily using a ICEM Surf as the primary CAD platform. It is a standard to represent a car hull with Bezier surfaces only. The reasons are manifold, but also opinionated. Primarily it is believed that Nurbs give away the level on control on a surface layout. The segments are connected on higher continuity automatically, but this does not guarantee a good overall surface. It is also believed that Nurbs tend to overcomplicate the surface model and as such introduce unnecessary error.
Interesting! We use Nurbs for granted, but barely know the implementation details…
See this for more detail on the algorithm. There are different algorithms on Nurbs and Bezier, but this gives a good overview on the curve part.
Nice, even contains curve curve intersections.
If needed, i can also recommend books on NURBS.
Please provide the books 
all available in a well sorted university library or “comparable”.
Rogers, David F. An Introduction to NURBS. Elsevier, 2001.
https://doi.org/10.1016/b978-1-55860-669-2.x5000-3
Piegl, Leslie Andrew, and Wayne Tiller. The NURBS Book. Springer, 1995.
https://doi.org/10.1007/978-3-642-97385-7
Farin, Gerald E. NURBS: From Projective Geometry to Practical Use. 2nd ed. CRC Press, 1999.
Patrikalakis, Nicholas M., and Takashi Maekawa,. Shape Interrogation for Computer Aided Design and Manufacturing. Springer, 2002
https://doi.org/10.1007/978-3-642-04074-0
if you have any questions reg. NURBS and stuff, just write a PM
As I understand it, NurbsCurve would rather store a collection of connected BezierCurves than needing to inherit from the latter.
C++ inheritance, not only in game dev a foe to be aware of. 
@Petras_Vestartas - some additional resources.
– Dale
Thank you