First off, have you set up your DNS records correctly so that your domain name points to your IP address?
Type Name Value TTL
A example.com your droplet IP address Automatic
CNAME www example.com Automatic
If that is done, then how is your server block defined? ....Does it look like this?
If you are set up like this, then I see no reason why you shouldn't arrive at the same location regardless of what is entered into the address bar. Yours may look a little different as I am using Nginx, not Apache.