TYPICALLY for all piston engines (for specifics see your airplane's AFM)...
Carbs: The boost pump and/or gravity supplies fuel to the carb. All you're doing is filling the float bowl at near-ambient pressure.
On a low-wing you need the pump, on a high-wing gravity alone is usually enough. The boost pump on a high wing is a back up to gravity...ie not strictly required unless you fly with sustained low g's, have some kind of flow resistance in the lines/filter to the carb, or experience a total gravity failure.
On some high wings gravity might not provide enough flow through the filter for sustained high-power ops (ie takeoff)...in which case boost pump use is mandatory.
Fuel Injection:The boost pump and/or gravity delivers fuel from the tanks to the inlet of the main fuel pump which requires a slight positive pressure head. The main pump boosts that pressure much higher, probably to about 30-50 psi for the injectors.
A failed boost pump may not stop the engine, but a failed main pump will. The boost pumps or gravity cannot supply more than 2-3 psi, nowhere near the 30-ish required for fuel injectors.
Again, read for AFM.