Fundamental reason for the color and flavor group to be the same? The answer to this question might just be a straight-up "no, it's just a coincidence", but since coincidences are rarely a thing in physics, I thought I'd ask.
Is there a fundamental reason why (take QCD, for example) the gauge (color) group $SU(N_c)$ is the same type of group as the global (flavor) group $SU(N_f)$? (the same question applies to the weak case with isospin instead of color)
I couldn't find an answer in my textbooks, and I couldn't think of anything except that maybe we just really like this group and even if the global flavor group could be described in several different ways we choose $SU(N)$ for practicality.
 A: It's just a coincidence.
Note that the original flavour $SU(3)$ permuting up, down and strange is broken by the differing masses, and the less badly broken $SU(2)$ is the isospin group. Both are thus approximate global symmetries. If you're fine with broken symmetries, you could add charm, bottom and top to go to $SU(6)$. However, the breaking gets progressively worse, and for the top, it would be completely useless.
The weak and strong groups $SU(3)$ and $SU(2)$, on the other hand, are exact gauged symmetries with associated gauge fields ($W$, $Z$, gluons), and so are completely different beasts.
Note also that in models beyond the standard model, gauge and flavour aspects are generally treated differently -- grand unified theories extend the gauge group to, e.g, $SU(5)$ or $SO(10)$, but the generations are just three copies of matter multiplets.
A: Recall that inertial mass was shown to be equal to gravitational mass  experimentally and for a long time this was thought of as a coincidence mainly because no-one could think of a better explanation. Then of course Einstein discovered his equivalence principle and the rest is history.
Likewise, this may pin to something more basic, the question is what. Perhaps string theory might have something to say here but I don't know enough string theory to say either way.
A: The fundamental reason is experimental observations. The quark model was slowly built up over the years  and the resonances measured in lab gave the surprising symmetries of the SU(3) group.
In general, the number of basic constituents defines the dimension n of SU(n). (As an example SU(2) for neutron and proton in nuclear physics,  fitted the data). For the three quarks, SU(3). If we had found experimentally four quarks SU(4) would have been chosen. The difference between SU(n) and U(n) is mathematical, stated here:

The more general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the special case.

italics mine.
