No, Illustrator is a vector drawing program. Inkscape or Corel Draw (if people even remember that) are direct competitors.

Krita has to to be compared to Photoshop because both are working on rasterized images. While Krita emphasizes drawing tools in its UI while Photoshop exposes manipulation tools more prominently, both programs aim to cover both sets of features. And Krita's core is actually much, much more advanced than what you would expect from a drawing program. I would actually love to see a UI for Krita that focuses more on manipulation, just to placate the "it's just for drawing" crowd.

I agree, Krita is more aimed at drawing than image manipulation (but as others said it's not akin to Illustrator)