\section* produces an unnumbered section, align*makes the environment unnumbered, which is comparable in a way. \newcommand*doesn't accept \par in its argument, which is different.
Stefan Kottwitz wrote:
Commonly, a star symbol
*means a version of a command that behaves differently from the original. That often means suppressing numbering but could also refer to special features.
This might answer my question, but perhaps there's more to say (and it's nice to have it as a separate question).
Is there anything all starred commands have in common? Why would one define a starred command as opposed to another, differently named command indicating their semantic difference in the names? It seems that their definitions are usually entirely independent from each other.
Further reading: