Muon neutrino and electron neutrino discoveries and their Nobel prizes In this lecture, around 44:00
https://youtu.be/KU94cMZif8Y?t=2635
The lecturer mentioned quickly that the 2nd neutrino (of muon) results in a Nobel prize earlier than the 1st neutrino (of electron's).

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*Puzzle: Could some experts please explain why and how the research results happened? Naively
the 2nd neutrino (of muon) is heavier than the 1st neutrino (of electron's). So why the 1st neutrino (of electron's) appears to be awarded or confirmed later?

 A: This belongs to the history of science, but Wikipedia is good for these questions:

In 1962 Leon M. Lederman, Melvin Schwartz and Jack Steinberger established by performing an experiment at the Brookhaven National Laboratory1 that more than one type of neutrino exists by first detecting interactions of the muon neutrino (already hypothesised with the name neutretto), which earned them the 1988 Nobel Prize

The italics show for what the prize was given, and it was not given just for the discovery of the muon neutrino, but for showing that more than one type of neutrino exists.
Then the committee thought that the separate discovery of the electron neutrino should also be honored, which had been seen experimentally earlier.

The electron neutrino was discovered by Clyde Cowan and Frederick Reines in 1956

In the 50's and 60's a great number of particle data was gathered confirming various models, few of the observations ended in prizes.
A: A small explanatory footnote to @anna's fine answer, which emphasizes the primacy of the LSS discovery, a major game-changer: it upended our understanding of particle interactions forever. The professionals at HSM would have more generic insights.
The 1995 NP awarded to Perl & Reines  was a bit special. (Cowan had died in 1974.)  The background is that Perl was overdue to get it for the τ lepton, whose Discovery was both surprising and important. Surprising, since no theorist had "ordered" it (unlike Reines' neutrino), and Perl had to thoughtfully  and heroically fight disbelief and build a solid  case for it. Important, since, once theorists accepted it, the prior anomaly cancellation of the SM (Bouchiat, Iliopoulos & Meyer 1972) argument all but dictated a full 3rd generation and the future discovery of the b, the t and the $\nu_\tau$. So, like the LSS  Discovery, it Really was a game-changer.
At that point, the Reines-Cowan observation was in danger of  being scandalously neglected, given the fact that, even though their (Pauli's, really) neutrino had been accepted indirectly, and figured in the sun burning, nuclear physics, weapons and reactors, etc, a direct observation appeared out of reach until their experiment. F & R made observation a reality, and initiated neutrino physics, experimentally speaking.
But it did not change anyone's mind on anything, I suspect. (I know could make people scream, but, analogously, few theorists changed their mind on anything upon the discovery of the W and Z; of course these had to be there. Note that NP also emphasized the accelerator, field-opening aspect of the observation.)
These are fine social/tribal points, and historians of science discuss them endlessly, but they provide background to your question and any presumption that the NP recognizes strictly "I was first" discoveries like a school prize. (But  I'd be opening a Pandora's box if I mused about Zweig or Bjorken, or the late Dyson..)
A: The 1956 discovery of electron antineutrino from nuclear reactions is credited to Clyde Cowan and Frederick Reines in their famous Savannah River experiment. They based the expected number of neutrino events to a parity-conserving weak interaction theory. Cowan and Reines reported the observed neutrino events consistent with parity-conserving theory.
However, the parity violation was confirmed in Wu experiment the following year. A parity-violating theory (so-called V$-$A theory) predicts the number of neutrinos to be twice the amount Cowan and Reines claimed. After these developments on the theory side, Reines insisted that he overestimated the detector efficiency. In their renewed experiment in 1960, Cowan and Reines reported that the number of neutrinos is consistent with parity-violating theory. One could interpret this inconsistency suspicious, and could be reason for the 39-year-delayed Nobel prize for the neutrino discovery.

Naively the 2nd neutrino (of muon) is heavier than the 1st neutrino (of electron's).

We have not been able to measure the masses of the neutrinos, only the upper limits. We also do not now which one of these two neutrinos is heavier, in a statistical sense.
