Instead of logically tying the endpoint of the network tunnel to the physical IP address, each tunnel is bound to a permanently associated IP address at the device. The mobile VPN software handles the necessary network-authentication and maintains the network sessions in a manner transparent to the application and to the user. The Host Identity Protocol (HIP), under study by the Internet Engineering Task Force, is designed to support mobility of hosts by separating the role of IP addresses for host identification from their locator functionality in an IP network. With HIP a mobile host maintains its logical connections established via the host identity identifier while associating with different IP addresses when roaming between access networks.
Once on the public internet, those packets travel through a bunch of computers. A separate request is made to a series of name servers to translate the DNS name ZDNet.com to an IP address. That information is sent back to your browser, which then sends the request, again, through a bunch of computers on the public internet. Eventually, it reaches the ZDNet infrastructure, which also routes those packets, then grabs a webpage (which is actually a bunch of separate elements), and sends all that back to you.
HotSpot Shield is a product that has had some ups and downs in terms of our editorial coverage. Back in 2016, they picked up some very positive coverage based on founder David Gorodyansky comments about protecting user privacy. Then, in 2017, a privacy group accused the company of spying on user traffic, an accusation the company flatly denies. Finally, just this year, ZDNet uncovered a flaw in the company's software that exposed users. Fortunately, that was fixed immediately.