I've seen that geth can be used to create a wallet address by doing
geth account new
Where is the wallet stored?
How can I backup this wallet in case I lose my computer?
What is the difference between geth and mist?
Where does mist store my wallet and how can I prevent myself from losing it as well?
Can I make transactions with any of them?
I will answer your questions as you asked them.
depending on if you have OS X, Windows, or Linux, here are the locations where they could be located:
~/Library/Ethereum/~/.ethereum/%APPDATA%/Ethereum/this folder holds the ethchain (Ethereum blockchain), and wallet keystore files (what allows you to access your wallet), as well as geth and other things. You can also navigate to it by navigating to the top of your screen in Mist and select File > Backup > Accounts like this
I'd like to clarify that your "wallet" is technically not "stored" anywhere, because the ethchain is a distributed public ledger anyone can view you wallet and funds. And you can take your keystore file (or other things such as private keys) and upload them to places like MyEtherWallet where you can send transactions. In other words, if you have access to the keystore, you have access to the wallet. That's why it's highly unrecommended to give your keystore file to anyone, even MyEtherWallet discourages it.
But technically, and in short, your wallet (or at least access to your wallet) is located in the keystore folder within the Ethereum folder which was located above.
In Mist, your wallet is automatically backed up in the keystore folder, (look here 'cause it was already answered), navigate to the top of your screen in Mist and select File > Backup > Accounts like this. If you'd like to keep your funds safe incase you lose your computer, open the keystore folder and copy all of the files to a USB or something of the sort. When you get your new computer and download Mist, just copy the keystore files from your USB device back to the keystore folder.
Mist is the friendly User Interface wallet which uses Go-Ethereum (also known as geth) to complete transactions and such. Geth is pretty much what "makes Mist go" (no pun intended ;) You don't need Mist to run geth but you need geth to run mist.
Geth and Mist store their keystore files in the same location which we already discussed above
with geth you first just run geth in a terminal. Then open another terminal and run geth attach. From there type in personal.unlockAccount(coinbase, "password") to unlock your account for transactions.
personal.unlockAccount(coinbase, "password")
then to do a transaction replace address (keep quotation marks) with address you want to send to, and value of eth you want to send.
eth.sendTransaction({from:eth.coinbase, to:"address", value: web3.toWei(1, "ether")})
In Mist simply click the send button on the top of the screen, select from which wallet, and paste the wallet address of who you want to send to, with the amount, then scroll and press send.
there ya have it folks.
Geth: It is multipurpose commandline tool that runs a full ethereum node implemented in Go. It offers three interfaces: 1) the command line subcommands and options 2) a Json-rpc server and 3) an interactive console.
geth provides commandline account management using the following command:
$ geth account <command> [options...] [arguments...]
All the information of every account is stored in the Data-Directory in go-ethereum package. For more information about refer Backup & Restore info. of account.
Mist: But mist is DApp which provides you two facilities it can act as browser or it can act as a cryptocurrency wallet.
Mist wallet provides us an user interface to manage account information and to store and send your Ether.
Mist is a powerful Ethereum special-purpose browser. It offers like a overall view of the Ethereum blockchain and all needed tools to interact with the blockchain component like Ether, DAO, smart contracts. Basically, Mist is a browser to access the DAPPS.
For more details on Mist refer: Step by step guide to Mist wallet.
