In the abstract of chapter 14 (Artificial Intelligence and Computational Intelligence: A Challenge for Power System Engineers) of the book Advanced Solutions in Power Systems: HVDC, FACTS, and Artificial Intelligence: HVDC, FACTS, and Artificial Intelligence the authors say
AI is concerned with decision‐making capabilities such as knowledge representation, search methods, inference techniques, heuristic reasoning, and machine learning. CI techniques include expert systems, fuzzy logic, genetic algorithms (GAs), and artificial neural networks (ANNs). CI can further involve adaptive mechanisms for intelligent behaviors in complex environments, such as the ability to adapt, generalize, abstract, discover, and associate.
AI is thus concerned with machine learning and CI is concerned with neural networks. However, neural networks, genetic algorithms and expert systems are, nowadays, widely considered or viewed as AI topics.
The paper What is Computational Intelligence and what could it become? (2003), by Duch Wlodzislaw, directly addresses the relationship between these two apparently distinct but highly related sub-fields. In the abstract, the author says
What is Computational Intelligence (CI) and what are its relations
with Artificial Intelligence (AI)? A brief survey of the scope of CI journals and
books with "computational intelligence" in their title shows that at present it is an umbrella for three core technologies (neural, fuzzy and evolutionary), their applications, and selected fashionable methods. At present, CI has no comprehensive foundations and is more a bag of tricks than a solid branch of science. The change of focus from methods to challenging problems is advocated, with CI defined as a part of computer science devoted to the solution of non-algoritmizable problems. In this view AI is a part of CI focused on problems related to higher cognitive functions, while the rest of the CI community works on problems related to perception and control, or lower cognitive functions. Grand challenges on both sides of this spectrum are addressed.
Therefore, AI is a sub-field of CI that focus on certain topics or approaches.
However, in the introduction of the same paper, the author states
Computational intelligence became a new buzzword that means different things to different people.
He further states
IEEE Computational Intelligence Society defines its subjects of interest as neural networks, fuzzy systems and evolutionary computation, including swarm intelligence. The approach taken by the journals and by the book authors is to treat computational intelligence as an umbrella under which more and more methods will be added. A good definition of the field is therefore impossible, because different people include or exclude different methods under the same CI heading.
And, in section 4
For many CI experts biological inspirations are very important, but even if biology is extended to include all neural, psychological, and evolutionary inspirations this will only cover the main themes (neural, fuzzy and evolutionary) that the CI community works on
In the same section
CI studies problems for which there are no effective algorithms, either because
it is not possible to formulate them or because they are NP-hard and thus not effective in real life applications. This is quite broad definition: computational intelligence is a branch of computer science studying problems for which there are no effective computational algorithms. Biological organisms solve such problems every day
A good part of CI research is concerned with low-level cognitive functions: perception, object recognition, signal analysis, discovery of structures in data, simple associations and control
There are thus many journals and books that fall into the computational intelligence category, but apparently there is no consensus on the meaning of the expression, which can also change over time. However, there are certain concepts that are often associated with CI, such as evolutionary algorithms, neural networks and fuzzy systems, which are partially inspired by biological systems. There are people that systematically differentiate the two (and often state that AI is more about higher-order cognitive functions), but not all people do it.
To conclude, CI and AI may (or not) be used interchangeably, or CI may refer to a subfield of AI (or vice-versa). Therefore, you should interpret the two expressions depending on the context.