What is difference between the different 'flavours' of neutrinos? Moreover, how-come scientist know that muon-neutrino are different from electron-neutrino when they didn't even know what the difference was? Did they interact differently with other particles?
 A: The Standard Model of paticle physics is a shorthand description of data gathered laboriously over half a century. From the first decays observed, in cosmic rays and cloud chambers, it was obvious that the mediating force was different than the electromagnetic or the nuclear force. Decays are  mediated by weak interactions, a conclusion that explained in a single format all observed decays. 

This image of neutron decay shows the process. It is a three body decay, and that is an experimental point because the momentum distributions of two body and three body decays are different. Using energy conservation and four momentum balance at first it seemed that the neutrinos had zero mass, and for many years that was the hypothesis, until neutrino oscillations were observed , but that is another story.
Eventually beams of neutrinos were created and it was affirmed that muon neutrinos scattering on protons created muons, whereas electron neutrinos created electrons. Yes they interact differently for each species, muon, electron , tau. Thus the ground was laid for the SU(3)xSU(2)xU(1) symmetry which encompasses all the quantum number data of the observed up to now particles in a single standard model.
A: Firstly, the mass of electron neutrino is different than muon neutrino. The mass of electron neutrino is less than 2.2 eV and the mass of muon neutrino is less than 170 KeV.
From the interaction side of view, electron neutrino is created along with the lepton "electron". On the other hand,muon neutrino is created with the lepton "muon". Most important part is that any flavors of neutrino is created only with its associated lepton.
eg: $n\rightarrow  p^++e^-+\bar{\nu}_e$
Here, you can see that electron anti-neutrino is created with the electron.
And you also see that in a reaction, suppose muon neutrino is created with electron.But,it is not possible because the conservation of lepton number then will be violated. 
