apache2 can't stop and nginx can't start

Really there's two questions here, so I'll try to answer them both:

1. Why do Apache and Nginx display the same webpage?

Take a close look at your configuration files. You will see that they both load the same content:

Apache is loading (document root): /var/www/html

Nginx is loading (root): /var/www/html;

This means both servers will show the same content, as they are loading the same file(s). You can change your "root" directory to be two different locations by editing your configuration files.

eg apache:

<VirtualHost *:8080>
    ServerAdmin webmaster@localhost
    DocumentRoot /var/www/html/apache
    ErrorLog ${APACHE_LOG_DIR}/error.log
    CustomLog ${APACHE_LOG_DIR}/access.log combined
</VirtualHost>

eg nginx:

server {
    listen       8080;
    server_name  127.0.0.1;
    root /var/www/html/nginx;
    index index.php index.html index.htm index.nginx-debian.html;

    location / {
            try_files $uri $uri/ =404;
    }

    error_page 404 /404.html;
    error_page 500 502 503 504 /50x.html;

    location = /50x.html {
            root /var/www/html/nginx;
    }

    location ~ \.php$ {
            try_files $uri =404;
            fastcgi_pass unix:/var/run/php5-fpm.sock;
            fastcgi_index index.php;
            fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
            include fastcgi_params;
    }
}

You'd then need to make each directory and put a file in them:

mkdir /var/www/html/nginx

mkdir /var/www/html/apache

And put content into each of these folders. It's also worth checking the permissions of each folder are appropriate for the web server to access them.

2. How do I check to see if Apache has stopped and Nginx has started

There's a simple way to check the status of each service. Assuming you're logged in as root:

service apache2 stop #Stop apache
service apache2 status #is apache still running?

You can also use the ps command to get the process list:

ps aux | grep -i apache

This effectively gets all running processes, and searches for any with the name apache.

You can then start nginx and check it's running:

service nginx start #start nginx
service nginx status #is nginx running?

(optionally another way to prove the process is running): ps aux | grep -i nginx

It's also possible to see which program is listening on which port:

netstat -ntlp

This will tell you the local address, port, and process name of everything listening for connections on your computer. You should see in this list either nginx or apache running with port 8080 (based on your configuration files) exposed.

You are using the same base path for web files (/var/www/html) and that is why the same content is displayed when using nginx or apache.

The easiest way to know who is responding to requests is to review the response headers:
curl -I 127.0.0.1
See what appears in front of Server.

This can also be done through the Network or Networking tabs in the developer console of web browsers, look for the value of "Server" in the response headers.

There can be a scenario where your apache service is stopped but even then what you are seeing is the /var/www/html directory as root and apache webpage. This is because of the directories in nginx - /etc/nginx/sites-enabled/ (consists of enabled virtual hosted servers) and /etc/nginx/sites-available/ (consists of available virtual hosted servers). One option is to delete/clean these directories with configuration files and other option is to just comment out the line in /etc/nginx/nginx.conf

##
# Virtual Host Configs
##

include /etc/nginx/conf.d/*.conf;

############Comment out the following line############

#include /etc/nginx/sites-enabled/*;

############Comment out the following line############

Then check for the following:

Nginx Configuration Test

sudo service nginx configtest

• Testing nginx configuration [ OK ]

or

sudo nginx -t

nginx: the configuration file /etc/nginx/nginx.conf syntax is ok
nginx: configuration file /etc/nginx/nginx.conf test is successful

Restart Nginx Service

sudo service nginx restart

• Restarting nginx nginx [ OK ]

Status of Nginx Service

sudo service nginx status

• nginx is running