Account
An account refers to an actor in the blockchain ecosystem.
Address
Each account has a unique identifier, called an "address". These addresses are derived from your public key.
Addresses on the Mosaic Chain and on the Polkadot System Chains start with "1".
Stash Account
This refers to the user's wallet that lives on their device. This usually stores Validator / Delegator NFTs.
DANGER
If you lose access to your stash account, you will lose access to all of your funds (NFTs and MOS) on the chain.
Controller Account
This is a hot wallet that lives on validator nodes, that handle daily tasks in the name of the stash account. But, for security reasons, it only has permission for a certain type of actions.
Controller permissions
A controller can only perform certain type of actions in the name of the stash account. For example, the controller account can chill or unchill the validator, but cannot transfer funds in the name of the stash account.
Proxy connection
The connection between the stash account and the controller account is called a proxy. It gives certain priviliges for the controller account to execute transactions in the name of the stash account.