The first runs in the VPN client app on your computer, so if the VPN connection fails while the VPN client app is running, that VPN client app can turn off the computer or mobile device's internet connection. However, if your VPN connection has failed because the VPN client app itself crashed, then the kill switch may not work, and your IP and data may leak onto the internet.
That attitude to the safety and privacy of personal data creates an enormous online security risk. Public Wi-Fi networks, which are ubiquitous and convenient, are unfortunately also highly convenient for attackers looking to compromise your personal information. How do you know, for example, that "starbucks_wifi_real" is actually the Wi-Fi network for the coffee shop? Anyone could have created that network, and they may have done so in order to lure victims into disclosing personal information over it. In fact, a popular security researcher prank is to create a network with the same name as a free, popular service and see how many devices will automatically connect because it appears safe.