Quoting from Wikipedia:

The GLM consists of three elements:

1. An exponential family of probability distributions.
2. A linear predictor $\eta=X \beta$
3. A link function $g$ such that $E(Y|X)=\mu=g^{-1}(\eta)$

There is no threshold inherent in a GLM. Once you have the model, you can make predictions of $\mu$ (sometimes called the "mean function") for any set of covariates $X$. For a binomial model that could be translated into a probability of class membership. Your application of the GLM might then involve a threshold for making class predictions, but that should be thought of as outside the GLM itself.

Quoting from Wikipedia:

The GLM consists of three elements:

1. An exponential family of probability distributions.
2. A linear predictor $\eta=X \beta$
3. A link function $g$ such that $E(Y|X)=\mu=g^{-1}(\eta)$

There is no threshold inherent in a GLM. Once you have the model, you can make predictions of $\mu$ (sometimes called the "mean function") for any set of covariates $X$. For a binomial model that could be translated into a probability of class membership. For a Poisson model, you are modeling counts directly.

Your application of a binomial GLM might then involve a threshold for making class predictions. Your application of a Poisson count model might involve translating counts into a rate per unit time, length, or area. But those applications should be thought of as outside the GLM itself.