Connected generally means the devices in question have successfully established communication
between each other. In other words, they are able to sent data packets between each other.
Connected no internet means communication is established between the devices, but this communication is not established with other interconnection of "outside servers" (internet)
or outside world. In this way, data packets are still sent and received between devices and not "outside server".
One of the devices e.g router, mobile (mobile APNs) provide this gateway in order to allow sending and receiving of these packets to "outside servers".
Several factors prevent this connection to the "outside servers":
- Firewall in one of the devices
- Firewall by ISP
- Blockage of the domain name system which translates host names to IP addresses
- Invalid APNs
- Incorrect DNS settings etc