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Illustrator and Photoshop both have the same function, Illustrator most people prefer it if they want to do graphics and change some of pictures into vectors. In addition, Photoshop can do the same but most people prefer it to do designs and lighting fixtures.
Illustrator is the most recommended software for Print Production.
For print production, in my opinion, would be Illustrator and Photoshop. There would be similar results with both but with Photoshop it would give your print a more realistic appeal. As for books and multiple pages I choose In Design