How can a neutrino detector tell the difference between the three types of neutrinos? In other words, what is the difference between the three flavors of neutrino?             Most articles talk about how they are created differently, but not about what actually distinguishes them from each other...           Also, one article mentioned their masses, but the three flavors were discovered and differentiated from each other before it was found that they had mass....
 A: The flavor of neutrinos, electron muon, tau, means that when they interact, from lepton number conservation they will create a muon, electron or tau, and that is how one distinguishes what type of neutrino hit the detector, to start with. By detecting an electron , a muon or a tau created in the detector by a trackless interaction( the neutrino leaves no track), the flavor is identified. 
There is this experiment, which managed to identify neutrino oscillations from the sun  even though the neutrino's of the sun energies were not enough to generate a real muons or  taus.

Unlike previous detectors, using heavy water would make the detector sensitive to two reactions, one reaction sensitive to all neutrino flavours, the other reaction sensitive to only electron neutrino. 

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In the charged current interaction, a neutrino converts the neutron in a deuteron to a proton. The neutrino is absorbed in the reaction and an electron is produced. Solar neutrinos have energies smaller than the mass of muons and tau leptons, so only electron neutrinos can participate in this reaction

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In the neutral current interaction, a neutrino dissociates the deuteron, breaking it into its constituent neutron and proton. The neutrino continues on with slightly less energy, and all three neutrino flavours are equally likely to participate in this interaction. 

A: 
What is the difference between the three flavors of neutrino?

You mentioned you know about the obvious differences in the modes of production and the differences in mass (or what we know about the masses, at least: mass hierarchy is still a problem), so let's put that aside and talk about other stuff. This may be singularly unhelpful because it's not a deep differentiation at all, but I'll still give it a shot. The different flavors of neutrinos have different lepton numbers, and this becomes important when you apply the theory that lepton number of each kind is conserved in interactions.
An electron neutrino has $L_e = +1$, but $L_\mu=0$ and $L_\tau=0$. Electrons have the same lepton numbers.
A muon neutrino has $L_\mu = +1$, but $L_e=0$ and $L_\tau=0$. Muons have the same lepton numbers.
The pattern extends to the tau neutrino and tau.
This becomes significant when we talk about interactions because lepton number conservation kind of helps to predict stuff. For example, consider the muon's decay mode into an electron, an electron antineutrino, and a muon neutrino.
\begin{alignat}{}
  \quad     & \mu^- & \rightarrow  & e^- & +  & \bar{\nu_e}  &    +   & \nu_\mu        && \\
  \quad     & (L_\mu=1) & \rightarrow & (L_e=1) & +& (L_e=-1)&+& (L_\mu=1)&& \\
\end{alignat}


How can a neutrino detector tell the difference between the three types of neutrinos?

One way to detect electron neutrinos is through observation of the charged-current interactions, which is one of the kinds of interactions displayed by neutrinos (the other being neutral-current; it  doesn't reveal anything about the flavor).
We can tell that the neutrino was an electron neutrino because at sufficiently high energies, an electron will be produced (high energies are needed to satisfy the mass-energy equivalence for the extra mass of the electron).
