As far as I understand, a symmetry can be broken explicitly (either by manually putting symmetry-violating terms in the Lagrangian or via an anomaly) or spontaneously. I want to focus on the second kind.
For a spontaneously broken symmetry (SSB), the Lagrangian is invariant under the symmetry transformation, but the ground state is not. So just by looking at the ground state, you don't see the symmetry, hence the alternative name hidden symmetry.
How are the terms "Dynamical", "Higgs" and "Goldstone" related to each other in the context of spontaneous symmetry breaking?
Some of my thoughts:
My nuclear physics lecture distinguishes global SSB ($\to$Goldstone, massless bosons) and local SSB ($\to$Higgs, bosons get "eaten"), no mention of "dynamical".
My QCD lecture states that SSB always leads to Goldstone bosons, and that there are two mechanisms how to achieve SSB: Higgs (bosons get "eaten") and dynamical breaking.
Wikipedia states that the Higgs mechanism and dynamical symmetry breaking are two ways of describing local SSB, whereas the Goldstone theorem applies for global SSB. They also list dynamical symmetry breaking for global symmetries if the breaking is due to quantum corrections (at the level of the effective action).
The Stanford Encyclopedia of Philosophy also distinguishes global SSB ($\to$Goldstone) and local SSB ($\to$Higgs, dynamical). In particular, they state that dynamical symmetry breaking means that the Higgs field is "phenomenological rather than fundamental", i.e. that the Higgs field are actually bound states from within the theory.