If I've researched this correctly, I believe that "Nikoli puzzles" are not a formal class of puzzles; rather the terms refers specifically to the publisher of these puzzles [1]. KenKen, on the other hand, was invented and trademarked separately by Tetsuya Miyamoto [2].

That being said, KenKen does seem to fall into a similar class of constraint-based, language-agnostic games.

[1] https://en.wikipedia.org/wiki/Nikoli_(publisher) [2] https://en.wikipedia.org/wiki/KenKen

Ken Ken differs from most of them in that it actually has math, whereas in the other games the numbers are really just symbols that could be anything (sudoku) or just counts (loopy/slitherlink, I think).