To use bitcoin then an internet connection is a must, don't you know that basic? Bitcoin is a digital currency in the first place.
To send and receive requires internet. Hardware wallets do not connect to the internet, but they can connect to a computer via USB and the computer can connect to the internet. The user's private keys never leave the hardware wallet; the hardware wallet can generate receiving addresses and sign send transactions. With a smartphone, the device storing private keys is directly connected to the internet, even if only temporarily.