Usage of the word "gauge" in these contexts This is probably a trivial question to someone with more knowledge than myself. I have met the word "gauge" now in the context of the gauge transformations that change the scalar and vector potentials of the electromagnetic field without changing the physical field itself:
$$A'=A+\nabla\lambda$$
$$\phi'=\phi-\frac{\partial\lambda}{\partial t}$$
My question is, is this related to its usage in the term "gauge boson". Do the gauage bosons in the standard model behave a certain way under the gauge transformations or is this just a example of the same word being used for multiple things?
 A: Yes it is.  Fields with this type of symmetry are called gauge fields.  They are classical in nature.  In the standard model of particle physics we see that the theory of electromagnetism can be thought of as arising from a symmetry of the matter particles described by a spinor field.  The equations for free spinors have a global symmetry.  In the case of ordinary charged particles this is a global phase.  Requiring that this global symmetry be local, i.e. that the phase can depend on position and time, gives rise to a new field, the 4-vector potential.  The kinetic terms for this new field are chosen to be the simplest non-trivial form that preserves the same symmetry.  This is mentioned to an extent in the comments.  Non of this is yet a QFT or a particle state.  This happens when we apply the prescription of quantum theory to the field equations, elevating them to operators.  The individual states are taken to be "particles" or quanta of the field.  In the case of Electromagnetism the classical gauge fields give rise to photons, the weak force gives W(+/-) and Z0 (weak bosons) and for he strong force we get gluons.  They are all "gauge" particles because the underlying classical theory is a gauge theory.  They are bosons because their intrinsic spin is an integer.  The spinors that describe matter have 1/2 integer spin and are called Fermions.  The designation of Fermion or bosn is related to the transformation properties of the field under Lorentz transformations (spatial rotations, and Lorentz boosts), and all fields that obey a space-time invariant theory will be either 1/2 integer or whole integer spin.  
