You may be confusing two different things:
Ground in an electronics context, as in Vss, as in the normal current return.
Earthing, aka Equipment Safety Grounding in a mains-electrical context, which is entirely a safety shield around what is effectively an isolated system of hot and neutral, with neutral being the usual current return.
There is never any current on Safety Ground except during a wiring fault. If the fault current is excessive, it will trip the circuit breaker. If not, it will hopefully flow enough to induce a GFCI trip, and not hurt any humans.
In mains wiring, conductors (hot and neutral) should be connected to Safety Ground absolutely never, with a solitary exception made out of necessity: an isolated system has nothing to keep the conductors from attaining an unexpected voltage. For instance leakage in a supply transformer could bias the entire isolated system at 2400V above ground, which would fail insulation. Or the isolated-system voltage could "rattle" due to capacitive coupling. So to prevent floating, the conductors are pegged to the earthing system, and the bonded conductor is defined as "neutral".
This neutral-ground bond is done in one single place to prevent redundant current paths (which themselves would be considered a ground fault). Before it was just good practice; now GFCI/RCD and AFCI protection devices absolutely require it.
Your first diagram is correct on the left and a code violation on the right: you didn't wire a neutral so you bootlegged neutral from ground. It will light only if somewhere off-diagram there is a neutral-ground bond. However if the source is GFCI/RCD protected, it will trip instantly.
Your second diagram shows an ungrounded system, much like you might have had in a 1946 house, except with the aforementioned neutral-ground bonding present. By modern standards you would want to extend that safety ground out to the loads, though GFCI/RCD protection will protect people if present.