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