Hi every one !

I'm new in cryptocurrency, I'm trying to understand it but there still one thing I didn't understand about wallets!
At first , I know there is cold and worm wallet.
The cold is a hardware that store coins in it
And the warm is a software or a site on internet that store coins on internet or in the laptop or mobile ( is what I already know right ?)
But what I'm trying to know about soft wallets like Bitpay, Enjin or BitCoin Core wallets , do they store bitcoins on the device or on internet ?
So if l have bitcoins in my mobile wallet and the mobile drop in water and gone!, did the coins gone too or I can get them back in a new mobile by the recovery key?
And I'm sorry for my weak English
As it has been explained well by the previous post the coins are NOT saved locally, but on the blockchain. Please ensure that you keep a copy of the private key, it is essential for BOTH recovering your coins and also to access from another wallet/device.