From the connecting user's perspective the difference is in what you use to start your connection. Both connections are started from the Machines panel in the same way. If you have the remote computer's IP address (public/private), you insert that into the Search field to start. If you have the remote computer's Machine Id, you insert that instead. 

Using the IP address to connect is free for the user that wants to connect. If you're inserting the Machine Id to connect, you need to be logged in to the Network Service and be in possession of a Network Subscription. 

From a technical perspective, if the target computer has been published on NoMachine Network, you can securely connect to it just by using its Machine Id. This is the best way to connect. No other action is necessary. Users, provided they have a Network Subscription, will be able to connect. If you prefer to make the computer available exclusively through the NoMachine Network service, you can even disable access over-IP by going to Server settings > Ports and enabling the box 'Let this server work only as a NoMachine Network host'.

Instead, if you want users to reach your computer using its IP address over the Internet, there may be some configurations necessary on the router and/or firewall. Please see the following article for details about that: https://kb.nomachine.com/AR04S01122.