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Knuths definition of , is mskipthinmuskip.

LaTeX changes this definition to

DeclareRobustCommand{,}{%

   relaxifmmodemskipthinmuskipelsethinspacefi

}

defthinspace{kern .16667em }

amsmath.sty says it's

DeclareRobustCommand{tmspace}[3]{%

  ifmmodemskip#1#2elsekern#1#3firelax}

renewcommand{,}{tmspace+thinmuskip{.1667em}}

I might understand LaTeX's point to make a command usable also in text mode. But what's the point of the redefinition by amsmath?

You should look at the full picture:

 152   │ ifxleavevmode@ifvmode@undefined

 153   │ DeclareRobustCommand{tmspace}[3]{%

 154   │   ifmmodemskip#1#2elsekern#1#3firelax}

 155   │ else

 156   │ DeclareRobustCommand{tmspace}[3]{%

 157   │   ifmmodemskip#1#2elseleavevmode@ifvmodekern#1#3firelax}

 158   │ fi

 159   │ renewcommand{,}{tmspace+thinmuskip{.1667em}}

 160   │ letthinspace,

 161   │ renewcommand{!}{tmspace-thinmuskip{.1667em}}

 162   │ letnegthinspace!

 163   │ renewcommand{:}{tmspace+medmuskip{.2222em}}

 164   │ letmedspace:

 165   │ newcommand{negmedspace}{tmspace-medmuskip{.2222em}}

 166   │ renewcommand{;}{tmspace+thickmuskip{.2777em}}

 167   │ letthickspace;

 168   │ newcommand{negthickspace}{tmspace-thickmuskip{.2777em}}

The two definitions of tmspace are due to recent decisions to make such commands start paragraph mode anyway. With a recent LaTeX kernel the second one will be used.

Contrast this with the code in the LaTeX kernel:

1619   │ DeclareRobustCommand{,}{%

1620   │    relaxifmmodemskipthinmuskipelsethinspacefi

1621   │ }



1630   │ defthinspace{leavevmode@ifvmodekern .16667em }

1631   │ defnegthinspace{leavevmode@ifvmodekern-.16667em }



4543   │ def>{mskipmedmuskip}

4544   │ def;{mskipthickmuskip}

4545   │ def!{mskip-thinmuskip}



4547   │ let:=>

The approach of amsmath is much more rational and cleaner. They also provide text mode equivalent of all macros, whereas ! cannot be used in text mode if amsmath is not loaded, and similarly for the others. The final result will be essentially the same. However, a , command will be translated into tmspace+thinmuskip{.1667em} when written in an auxiliary file, instead of ,. Not really a big deal.