OK, so both neutinos and antineutrinos are subatomic particles emitted during various types of radioactive decay with no charge and very little mass.
My question(s) is(are) this(these): What is the difference between the two, and how were they both discovered?
Actually, the question of whether neutrinos and antineutrinos are different particles is still up in the air (disclaimer: I am not a particle physicist, although I am a physicist.) Until the discovery of neutrino mass, most physicists assumed that neutrinos were something called “Dirac spinors”, which means (among other things) that the neutrino and the anti-neutrino are different particles (just as the electron and the positron are different particles.) Since the observation of neutrino mass, though, a fair number of particle physicists have been advocating the idea that neutrinos are “Majorana spinors”, which would imply that the neutrino is its own antiparticle. (This isn’t as far-fetched as it would sound – the photon, for instance, is its own antiparticle.) To the best of my knowledge, the question hasn’t been settled conclusively either way.
As to how you detect neutrinos: since they interact very weakly with matter, you need a lot of matter that you can very closely observe to be able to see their effects, and you need that matter in an environment that’s well-shielded from other influences. So generally what you do to detect neutrinos is to go deep underground in an abandoned mine, fill up a big tank with heavy water or dry cleaning fluid and watch it very closely.
Oh, almost forgot: here’s a good review of the neutrino mass problem.
It’s worse than that: It’s been settled conclusively both ways. That is to say, some folks say they’ve absolutely, without a doubt, proven that they’re Majorana, and some folks say they’ve absolutely, without a doubt, proven that they’re Dirac. I’m not a particle physicist, either, and when the question was relevant in some recent research I did, I dodged the issue by just treating both cases.
Assuming that they are different, the difference is in something called “lepton number”. Leptons are particles like the electron (and also the muon and tauon, electron-like particles with higher mass) and neutrinos corresponding to each (so you have an electron neutrino, a mu neutrino, and a tau neutrino). Each of these has a lepton number of 1, and their antiparticles each have lepton number -1. Lepton numbers add, and are conserved.
For instance, in beta decay, a neutron decays into a proton, an electron, and an electron antineutrino. The neutron isn’t a lepton, so you start with a lepton number of 0. The electron is a lepton, with lepton number +1, and the antineutrino is an antilepton, with lepton number -1, so the total after the decay is still 0.
Note that this only works if the neutrino is Dirac. If the neutrino is Majorana, then lepton number is not well-defined, so one can’t talk about its value or whether it’s conserved.
Also, if neutrinos have antiparticles, then the six known leptons (electron & electron neutrino, muon & muon neutrino, tauon & tauon neutrino, and all their antis) neatly mirror the six known quarks: up & down, strange & charmed, and top & bottom, and all their antis.