Understanding alias (used as rewrite)

[E.B.]

Hi, I'm confused about the details of "alias" used as
a kind of rewrite (which should be more efficient as
I understand it, as long as its appropriately used).

I found I can do this:

location = /path/number/one.html {
  alias /some/other/path/script.php;
  include fastcgi.conf;
}

So I was confucsed why this not working:

location ^~ /my-long-prefix-goes-here  {
  alias /another/different/path/anotherscript.php;
  include fastcgi.conf;
}

In other words, alias of exact location match does
a cheap "rewrite" perfectly. But now I want to match
addresses like:

/my-long-prefix-goes-here
/my-long-prefix-goes-herexxx
/my-long-prefix-goes-here/
/my-long-prefix-goes-here/filename

Only the first one works, the others are 404. Is
Nginx adding the tail end of the matched prefix
to the aliased location? I tried to make my alias:

alias /another/different/path/anotehrscript.php?;

so the stuff on the end turns into a query arg which
php can ignore. But that didn't work.

I also tried to use regex to match the location:

location ~ ^/my-long-prefix-goes-here  {

But now NONE of the addresses work - even the
exact match is 404. Why??

I found this was the only way to make it work:

root /another/different/path;
rewrite ^(.*)$ /anotehrscript.php break;

In this situation is rewrite the only solution?