How to make 2 servers on nginx. One just accessible by IP and another one just by localhost

Question

I have a 2 folders with different sites on my server

One is /var/www/html which I want to be accessible by my IP:80 other is denny

One is /var/www/cats which I want to be accessible by my localhost:80 and other is denny

How could I figure out it in my nginx settings?

UPD. 1

Well I have 2 configs

sudo nano /etc/nginx/sites-enabled/default
server {
        listen 122.111.111.40:80;
        root /var/www/html/;
        index /;
        server_name 122.111.111.40;
        location / {
                allow 122.111.111.40;
                deny all;
                autoindex on;
                index index.php;
                try_files $uri /index.html /index.php;
        }
        location ~ \.php$ {
                include snippets/fastcgi-php.conf;
                fastcgi_pass unix:/run/php/php7.0-fpm.sock;
        }
        location ~ /\.ht {
                deny all;
        }
}



sudo nano /etc/nginx/sites-enabled/cats
server {
        listen   127.0.0.1:80;
        root /var/www/cats/;
        index /index.php;
        server_name localhost;
        location / {
                allow 127.0.0.1;
                deny all;
                autoindex on;
                index index.php;
                try_files $uri /index.html /index.php;
        }
        location ~ \.php$ {
                include snippets/fastcgi-php.conf;
                fastcgi_pass unix:/run/php/php7.0-fpm.sock;
        }
        location ~ /\.ht {
                deny all;
        }
}

While I access localhost it's okay. I have my route to cats/index.php folder working fine. While I route to my IP I have 403 Forbidden It's says

2020/09/22 05:44:02 [error] 17563#17563: *853 access forbidden by rule, client: 115.111.11.111, server: localhost, request: "GET / HTTP/1.1", host: "122.111.111.40".

So some problem with my config. But I could not understand which one. If I will request my IP/index.php I will see an index page of cats/index.php but that's should be html/index.php. Right?

UPD. 2

Adding sudo nano /etc/nginx/snippets/fastcgi-php.conf

# regex to split $uri to $fastcgi_script_name and $fastcgi_path
fastcgi_split_path_info ^(.+\.php)(/.+)$;

# Check that the PHP script exists before passing it
try_files $fastcgi_script_name =404;

# Bypass the fact that try_files resets $fastcgi_path_info
# see: http://trac.nginx.org/nginx/ticket/321
set $path_info $fastcgi_path_info;
fastcgi_param PATH_INFO $path_info;

fastcgi_index index.php;
include fastcgi.conf;

UPD. 3

Adding sudo nano /etc/nginx/fastcgi.conf

fastcgi_param  SCRIPT_FILENAME    $document_root$fastcgi_script_name;
fastcgi_param  QUERY_STRING       $query_string;
fastcgi_param  REQUEST_METHOD     $request_method;
fastcgi_param  CONTENT_TYPE       $content_type;
fastcgi_param  CONTENT_LENGTH     $content_length;

fastcgi_param  SCRIPT_NAME        $fastcgi_script_name;
fastcgi_param  REQUEST_URI        $request_uri;
fastcgi_param  DOCUMENT_URI       $document_uri;
fastcgi_param  DOCUMENT_ROOT      $document_root;
fastcgi_param  SERVER_PROTOCOL    $server_protocol;
fastcgi_param  REQUEST_SCHEME     $scheme;
fastcgi_param  HTTPS              $https if_not_empty;

fastcgi_param  GATEWAY_INTERFACE  CGI/1.1;
fastcgi_param  SERVER_SOFTWARE    nginx/$nginx_version;

fastcgi_param  REMOTE_ADDR        $remote_addr;
fastcgi_param  REMOTE_PORT        $remote_port;
fastcgi_param  SERVER_ADDR        $server_addr;
fastcgi_param  SERVER_PORT        $server_port;
fastcgi_param  SERVER_NAME        $server_name;

# PHP only, required if PHP was built with --enable-force-cgi-redirect
fastcgi_param  REDIRECT_STATUS    200;

Answer 1

Assuming you don't have any other sites, following config should work:

server {
    listen <ip>:80;
    root /var/www/html;
    ...
}
server {
    listen 127.0.0.1:80;
    root /var/www/cats;
    ...
}