I haven’t seen the actual reason it makes noise during operation mentioned yet. The core inside of conductors are thin sheets of metal glued together. They use thin sheets to minimize energy losses, because the core develops currents that oppose the induction. This current and power loss produces heat. The heat causes the sheets to expand and contract at slightly different amounts. This creates the humming sound.
Clicks are usually switches or relays, which have a physical contact that moves to turn the power on and off. The click is primarily the contacts slamming shut and open, but there is often an arc which will make sound too.
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