Unifications in physics

I find the term "unification" is very loosely used by lay people and physicists, alike.
The term carries extra weight because it is supposed to be the Holy Grail of physics, and so people like to bring it up in casual conversations.  The other possible reason is that it is indeed a confusing idea, and probably the idea of "unification:" is itself not unified.

The most elegant illustration of unification in physics is of course Maxwell's equations for electromagnetism, where electricity and magnetism are seen to be basically different manifestations of the same underlying phenomenon. That they were related was already known from the experimental work by Faraday and others, but post-Maxwell we know that the complete theory for them is a single, complete set of equations that tell us how electric and magnetic fields come about. This unification is manifest even at the notational level, as they now get written together in compact fashion as a single four-tensor. Electric and magnetic fields now seamlessly Lorentz transform into each other when we change frames of reference.  This is according to me the paradigm for unification. When forces which were previously thought to be different, are shown to have a shared physical origin (both electric and magnetic fields come from electric charge) and are described by the same mathematical formalism.


However the later unifications achieved in particle physics are not so simple.  They are described by one mathematical theory SU(3)*SU(2)*U(1) alright, but I do not quite understand the physical aspects of it.  The strong, weak and electromagnetic forces are still distinct entities with different carrier particles. Wiki puts it this way (talking about electroweak theory) : "Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force."  Actually I am not even sure how we arrived at this dogma that there are only four distinct forces in nature.

There are many examples, where a physicist might be tempted to use "unification" in its everyday English sense.  Two physically very different phenomenon could be governed by the same differential equation.
Quantum particles and stochastic systems both are inherently probabilistic - hence the Schrodinger and Fokker-Planck equations are mathematically identical.  The same phenomenological theory applies to  magnetism and superconductivity and gas-liquid transitions while they are microscopically entirely different systems. This is called "universality", not "unification".  This also leads us to the old reductionism-vs-emergence debate. Why at all is simplicity and unification and a bottom-up approach necessary?  Nowadays they even speak of gravitation as an emergent phenomenon.

I think I should go read more about this, especially the standard model side of this, and come back with a more erudite post by the end of summer.