The correct differentiation between the lysogenic and lytic cycles is:
The host cell is destroyed during the lytic cycle.
In the lytic cycle, the virus invades the host cell, replicates its genetic material, produces new viruses, and ultimately causes the host cell to lyse (burst), which releases the new viral progeny.
In contrast, during the lysogenic cycle, the viral DNA integrates into the host cell's genome and replicates along with the host's DNA without causing immediate harm to the host. The virus might remain dormant for an extended period until it activates and enters the lytic cycle.
The other statements provided are not accurate in their respective contexts. For instance, viral proteins are typically synthesized during the lytic cycle, and the virus injects its genetic material during both cycles, but the integration within the lysogenic cycle is unique.