Each time you request blockchain data from a wallet, the server may be able to view your IP address and connect this to the address data requested. Each wallet handles data requests differently. If privacy is important to you, use a wallet that downloads the whole blockchain like Bitcoin Core or Armory. Tor can be used with other wallets to shield your IP address, but this doesn’t prevent a server from tying a group of addresses to one identity. For more information, check out the Open Bitcoin Privacy Project for wallet rankings based on privacy.
Full clients verify transactions directly by downloading a full copy of the blockchain (over 150 GB As of January 2018). They are the most secure and reliable way of using the network, as trust in external parties is not required. Full clients check the validity of mined blocks, preventing them from transacting on a chain that breaks or alters network rules. Because of its size and complexity, downloading and verifying the entire blockchain is not suitable for all computing devices.
The first wallet program, simply named Bitcoin, and sometimes referred to as the Satoshi client, was released in 2009 by Satoshi Nakamoto as open-source code. In version 0.5 the client moved from the wxWidgets user interface toolkit to Qt, and the whole bundle was referred to as Bitcoin-Qt. After the release of version 0.9, the software bundle was renamed Bitcoin Core to distinguish itself from the underlying network.
So that’s Bitcoin mining in a nutshell. It’s called mining because of the fact that this process helps “mine” new Bitcoins from the system. But if you think about it, the mining part is just a by-product of the transaction confirmation process. So the name is a bit misleading, since the main goal of mining is to maintain the ledger in a decentralized manner.