I've only used block chain. Info and coin base. Is block chain my client?
What is the difference between address and keys?
What client should I use so I always have my bitcoins and the client is only doing the transaction nothing else?
Do I get my private key and public key from this client?
Blockchain is a web wallet, and you might also call it your client.
Address = Thing people need to send bitcoins to you,
Private Key = Thing you need to spend bitcoins (Keep this secret)
And you can export the private key. The public key is technically just the address.
And also, computer failure, lost passwords, and file corruption can lead to the loss of your keys, so you should back them up.