Bitcoins are stored on wallet which essentially serving as their own bank for the user. A wallet program is provided by the Bitcoin network which allows users to transfer bitcoin between one another. Wallets can be stored in a variety of ways
1. online wallet provider
2. CPU wallet
Paper wallet
3. Mobile wallet device
4.Smartphone apps
Well, I'm guessing you are trying to offer some helpful information? You have some inacuracies in there so maybe I can help clarify.
*Bitcoins are not stored in a wallet. They are always on the blockchain which is a public ledger that anyone can see. Bitcoin is moved around through addresses on the ledger and you can access those addresses by using a key. Over time, to make it easy, the community has called the address and key a wallet (much easier to say and understand).
So a "wallet program" is kind of provided by the bitcoin network but "wallet program" isn't entirely accurate.
*So while the addresses on the ledger are public information, the key to access an address is what you can keep private to make that address "yours". When people talk about different wallets, they are all just different ways to keep your address and key.
*The most secure and effective way to make sure your bitcoins are safe, is to skip all those cpu/web/app wallets and just write down your address and key on a piece of paper, and then put it in a metal safe in your home. The blockchain is open source and public, you can access it from anywhere as long as you have your key.
*If you think that storing it on a piece of paper is too ghetto, the 2nd most secure way to store your bitcoins is using a hardware wallet like Trezor or Ledger.
*I personally do not recommend using any wallet that is on your phone, browser, or computer. Harware wallets or paper wallets are the way to go.