Pre-/Post-Market Trading
There is market activity outside of 'normal business hours.' During these hours, trades are being executed and reported, but they are not part of the official market activity that the system is designed to report.
This 'interday' trading is comparatively extremely low volume, with all that implies, but is frequently used by traders as an early signal of how the market will react to news (typically earnings calls) when the next market session opens.
Many brokerages, even for individuals, allow the placing of pre-market or post-market orders (my own has them expire as soon as the market opens) but these will not have the full functionality available during proper market hours and are offered as an amenity rather than core service.
The sun indicates pre-market, the early morning hours before markets officially open. The moon symbol indicates 'post-market' the evening hours after the market has closed but while trades are still executing.
These vanish at, in your example, 09:30EST, because then the market has opened and so whatever price signal it's sending is automatically more relevant than whatever happened in the pre- period. You'll see the moon symbol appear promptly at 16:00:01.
The numbers above the sun/moon line represent the "official" closing price at the market bell for the prior business day.
So for GOOGL in the top image. The prior day's closing price was $158.29, down $0.96 (or 0.6%) from the day before that. In the pre-market session, the last price cleared was $161.26, representing a gain of $2.97 (or 1.88%) from the prior day close of $158.29.