Is it wrong that splines are only available in GAM-models, and not in GLM-models? I heard this a while back, and wonder if this is just a misconception, or has some truth to it. Here is an illustration:
You are mistaken. Splines have a linear representation using derived covariates. As an example, a quadratic trend is non-linear, but can be modeled in a linear model by taking: $E[Y|X] = \beta_0 + \beta_1 X + \beta_2 X^2$, thus $X$ and its square are input into a linear model.
The spline can simply be seen as a sophisticated parametrization of one or more continuously or pseudo-continuously valued covariates.
@AdamO's answer is correct, in that spline-based fits can certainly be done in the standard GLM framework. That's not to say that GAM's are just a special case of GLM's though! While there are a series of models that exactly identical and can be framed as both a GAM or as a GLM with a spline expansion of the covariates, there are some GAM models that are not available in the standard GLM framework.
For example, one could fit a GAM model using a smoothing spline for each of the covariates. This basically results in a spline expansion of the variables, but with a penalty on the second derivatives. This results in a model that is a bit outside the standard GLM framework.
In addition, it's often considered standard procedure, and is built into most GAM libraries, to fit smoothing parameters (i.e. spline degrees of freedom, etc.) by optimizing various measures of out of sample errors, while the GLM formulation typically considers the covariate space fixed.