This subject is discussed in Prof. Mark E. Glickman, [A Comprehensive Guide To Chess Ratings][1].

  [1]: https://www.glicko.net/research/acjpaper.pdf

> It appears as though there is very little distinction between the
> shape of the logistic distribution in Figure 2 and the normal
> distribution in Figure 4. Figure 5 shows both curves superimposed,
> with the logistic distribution drawn as a solid line. In fact,
> statistics professor Hal Stern in a 1992 article[11] has shown that
> when analyzing paired comparison data it makes virtually no difference
> whether one assumes the logistic distribution or the normal
> distribution for differences in players' strengths. So, empirically,
> the choice between the Bradley-Terry model and the Thurstone-Mosteller
> model is a moot issue. **Mathematically, however, the Bradley-Terry
> model tends to be more tractable to work with.** This is the most likely
> reason that most organizations administering a probabilistic rating
> system (e.g., FIDE, USCF) use the Bradley-Terry model, which uses the
> logistic distribution assumption, rather than the Thurstone-Mosteller
> model, which uses the normal distribution assumption.

It is easy to see from the "FIDE Rating Regulations 2022" that the original Elo tables are still in use by FIDE.