Actaea

Although, to be honest, I don't quite understand why the concept of artificial intelligence isn't identical to the ability to think creatively (that is, to solve creative problems, including the Turing test, which is also a creative task, just like everything else). Or does it mean that creative tasks can be solved not creatively, but with the help of pre-compiled algorithms and "by the book"?

Hmm...
1) Creative tasks are creative precisely because there is no clear analytical algorithm for them.
2) Thinking and successfully solving creative tasks are different things.
3) In most cases (and perhaps in all, I don't know), we are talking about self-learning systems. That is, the creator of such a system develops a heuristic algorithm, with which the system learns to solve problems in a specific area.
4) What are some examples of creative tasks?
Well, one of the most famous is:
"A doctor knows the symptoms; he must make a diagnosis."
As you understand, there are no exact methods. Such a task is traditionally solved only by a person. However, about ten years ago, systems were developed and implemented that can make a diagnosis with an accuracy of ~97%. First, such a system is trained on a given set of input data, then the correctness of the training is tested on other sets, and only then can it work.
Or other tasks.
For example, you need to recognize where a human face is in a photograph, or recognize text of poor quality.
All this is in the field of artificial intelligence.

This is in response to your question. The concept of thinking creatively is not identical to the ability to solve creative tasks. A program doesn't think, but it will successfully cope with tasks if it is taught.

5) Do you know anything about neural networks? This is also one of the rapidly developing areas. Well, this is just one of the implementation methods that allows you to teach a program something.