What motivates, justifies, gives rise to the differences between the Gumbel, Fréchet, and Weibull distributions? Glen_b's comment indicates that they are distributions for extreme values generated by different kinds of distributions in IID sequences. What are those different kinds? [EDITed in response to Glen_b's comment.]
Feel free to point me to other sources.
[Background: I'm just beginning to learn a little bit of extreme value theory (mostly by working through early sections Reiss & Thomas's Statistical Analysis of Extreme Values 2nd ed.). I understand the mathematical definitions of the fully parameterized Gumbel, Fréchet, and Weibull distributions, how they can all be viewed as special cases of a generalized Extreme Value distribution, and that for some parameter combinations a Fréchet or Weibull distribution can be close to a Gumbel distribution. I'm trying to get insight into these distributions' differences at a more conceptual level.]
[I have no reason to doubt that Glen_b is right, but just in case, here are parts of the original question that no longer seem relevant: Are there real-world examples or mathematical contexts that help to motivate, for example, the use of a Fréchet distribution as opposed to a Gumbel distribution? (cf. radioactive particle emissions as motivation for the Poisson distribution.) Or might it be useful to see the three distributions as derived from some other distributions, perhaps as a limit as some parameters go to 0 or $\infty$? (cf. Poisson distribution as a limit of a binomial distribution.) A closely related question: Why would you choose to model extreme values with one of the three distributions rather than the other two (other than simply thinking that the data look like they'd fit one distribution better)?]