are modern prolog just a layer on top of the old semantics or somehow an incompatible paradigm ?
The set of CLP languages is generally implemented as a superset or add-on package(s) to a Prolog implementation. For example, SICStus Prolog and SWI-Prolog have CLP modules, e.g.:
https://sicstus.sics.se/sicstus/docs/3.7.1/html/sicstus_32.h...
http://www.swi-prolog.org/pldoc/man?section=clp
and "Constraint Handling Rules(CHR):
http://www.swi-prolog.org/pldoc/man?section=chr
To the best of my knowledge the modules are written in Prolog. A look at those links will give you an idea of how CLP is used. There are modules available for CLP(X) where X is one of:
B = boolean,
Z = integers,
Q = rational numbers,
R = real(floating point) numbers,
FD = finite domains (see "CLP(FD) Constraint Logic Programming over Finite Domains" http://www.pathwayslms.com/swipltuts/clpfd/clpfd.html )
etc.
One can understand how constraining the domain of interest (reducing the search space) to say, the integers, might make search more efficient.
Devising and implementing such suitable interface predicates is quite hard, and only a very small number of Prolog systems have succeeded with this so far.
For example, the SWI interface for CLP is too limited in practice, and its constraint solvers have elementary mistakes also because of the limitations of the interface predicates it provides.
In contrast, SICStus Prolog provides a much more general interface to attributed variables that supports all widely used constraint solvers (finite domains, Boolean variables, rational numbers etc.) with good performance and no known mistakes.
The tutorial you link to has several rather severe shortcomings, and I cannot recommend it for learning CLP(FD). Please see my profile page if you are interested in Prolog resources.
An example of such a construct is dif/2, which is a constraint that was provided in even the very first Prolog system, sometimes called Prolog 0, several decades ago. However, it was not widely available in Prolog systems until much more recently, even though professional Prolog systems such as SICStus have provided it for longer. Also arithmetic constraints were available in early implementations such as Prolog IV. So, in a sense, we are now going "back to the roots" of Prolog by making very old features widely available.
In my personal view, calling modern Prolog an "incompatible paradigm" with the way that Prolog is still being taught is not completely fitting, yet still more right than wrong: The new features are not meant to be used "on top" of old features, but instead! When using modern Prolog features to their fullest extent, you can completely eschew those language constructs that traditionally cause the worst problems for beginners.
Moded arithmetic is a prime example for this, which can be replaced completely by arithmetic constraints in modern Prolog systems. dif/2 is also a good example, which lets you avoid (\+)/1 in many cases by using a more general predicate instead.
Due to their operational semantics that is very hard to explain and understand, rather limited constructs often take significant room in many Prolog courses, and replacing them by more modern alternatives will entail a paradigm shift towards better methods and also make room for even more new material that can be covered instead. This is because on top of being more general, the new language constructs are often also easier to understand for beginners.
That is very powerful indeed. From incompetently playing around with stuff like that, my impression was that "constraints everywhere" is also extremely slow. That's not surprising, there's a lot of machinery working below the surface to deliver all that power. To recover performance whenever the full generality of the paradigm is not needed, I expect we'd need to work hard, say very smart static analysis, or JIT specialization, or...
But certainly my incompetence made me miss a lot. If you know how "constraints everywhere" can be made "fast everywhere", I'd love to hear about it:-)