There is a very important difference between the root and the alias directives. This difference exists in the way the path specified in the root or the alias is processed.

root

alias

To illustrate:

Let's say we have the config

location /static/ {
    root /var/www/app/static/;
    autoindex off;
}

In this case the final path that Nginx will derive will be

/var/www/app/static/static

This is going to return 404 since there is no static/ within static/

This is because the location part is appended to the path specified in the root. Hence, with root, the correct way is

location /static/ {
    root /var/www/app/;
    autoindex off;
}

On the other hand, with alias, the location part gets dropped. So for the config

location /static/ {
    alias /var/www/app/static/;
    autoindex off;           ↑
}                            |
                             pay attention to this trailing slash

the final path will correctly be formed as

/var/www/app/static

In a way this makes sense. The alias just lets you define a new path to represent an existing "real" path. The location part is that new path, and so it gets replaced with the real path. Think of it as a symlink.

Root, on the other hand is not a new path, it contains some information that has to be collated with some other info to make the final path. And so, the location part is used, not dropped.

The case for trailing slash in alias

There is no definitive guideline about whether a trailing slash is mandatory per Nginx documentation, but a common observation by people here and elsewhere seems to indicate that it is.

A few more places have discussed this, not conclusively though.

https://serverfault.com/questions/376162/how-can-i-create-a-location-in-nginx-that-works-with-and-without-a-trailing-slas

https://serverfault.com/questions/375602/why-is-my-nginx-alias-not-working