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I understand that multinomial tests and binomial tests are both likelihood ratio tests for testing if a sample has a categorical or Bernoulli distribution. G tests are also likelihood ratio tests for testing if a sample has a specific distribution. so my question is: do multinomial and binomial tests belong to G tests?

Thanks!

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Yes, they are. In particular, take a look at the formula on that page for the multinomial test where it refers to the likelihood ratio test, a few lines down from the top. The $x_i$ there is the same as the $O_i$ on the G^2 test, and if you consider the $pi_i$ equal to $O_i/n$, and the $p_i$ equal to $E_i/n$, then you'll see that it is precisely the G Test.

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