how do I redirect a location to another but not changing its URL in Nginx

There are so many ways to do it...

The most simple is

rewrite ^/product/ /product.php;

at the server context. Your original request URI (i.e. /product/1.html) will be available for product.php script as $_SERVER['REQUEST_URI'] array item value.

You can also use rewrite directive at the location context, this can be slightly (very slightly) more performant:

location /product/ {
    rewrite ^ /product.php last;
}

If you want, you can get product code and pass it to your product.php script as a query argument:

rewrite ^/product/(.*)\.html$ /product.php?product=$1;

or

location /product/ {
    rewrite ^/product/(.*)\.html$ /product.php?product=$1 last;
}

This way your product code (1 for the /product/1.html URI, 2 for the /product/2.html URI, etc.) will be available for product.php script as $_GET['product'] array item value.

You can even define an individual FastCGI handler for this:

location /product/ {
    include fastcgi_params;
    fastcgi_param SCRIPT_FILENAME $document_root/product.php;
    fastcgi_pass <fastcgi_upstream_or_socket>;
}

(original request URI will be available via $_SERVER['REQUEST_URI']), or if you want for product code to be available via $_GET['product']:

location ~ /product/(.*)\.html$ {
    include fastcgi_params;
    fastcgi_param SCRIPT_FILENAME $document_root/product.php;
    fastcgi_param QUERY_STRING product=$1;
    fastcgi_pass <fastcgi_upstream_or_socket>;
}