What each reset erases and keeps

The five, gentlest first

Action	Where	Coins and settings	Wi-Fi network	Restarts?	Welcome screens again?
`Restart`	Device → Reset	kept	kept	yes	no
`Factory defaults`	Device → My settings → Restore from	back to shipped	kept	no	no
`Start over (keep Wi-Fi)`	Device → Reset → Erase…	erased	kept, with any fixed address	yes	yes
`Erase Wi-Fi`	Device → Reset → Wi-Fi…	kept	erased	yes, into setup	no
`Everything, (FACTORY RESET)`	Device → Reset → Erase…, or five quick restarts	erased	erased, fixed address too	yes, into setup	yes

Wi-Fi erased: the ticker is restarting into first-time setup, coins and display settings are kept 9:41192.168.1.107 Factory Reset Done: Wi-Fi and settings erased, restarting for setup

What “kept” means for each

Restart writes nothing. It is the same as unplugging and replugging.
Factory defaults rewrites only what you can change on the page: the coin list, colors, brightness and timings. The ticker’s own history (that it has been set up, that it has taken an update) is untouched, and the screen redraws without a restart.
Start over (keep Wi-Fi) clears the whole settings store and restarts, then restores three things on the way out: the Wi-Fi network, a fixed address if one was set, and the record that this ticker has been set up and has reached its server. That last record is what keeps the ticker from behaving like a never-set-up unit on its Wi-Fi.
Erase Wi-Fi erases the network and the fixed address and restarts straight into setup; every coin and display setting survives. See Erase the Wi-Fi and set up again.
Factory reset erases the settings store, the Wi-Fi network, the fixed address, and the live brightness and colorset cache. It keeps the downloaded coin logos when they pass their check, so the ticker does not spend its first minutes on your network fetching artwork again.

Two things every reset keeps

The icon pack is kept unless it has been found faulty, and the note that a faulty pack was quarantined survives every erase, so a bad download cannot be fetched again by a reset. The ticker’s record of having taken a firmware update also survives; it is a fact about the device, not a setting.