Both are methods of viral multiplication inside the host cell.
Lytic cycle (which is more common) includes steps like:
1. Infection of the host cell-virus attaches to the receptor of the host cell, penetrates it and releases its genetic material into the host cell.
2. Virus Multiplication-Virus incorporated its genetic material into the host’s and uses its metabolism to multiply. Viral genetic material replicates separately from the host DNA.
3. Cell Destruction- Virus releases an enzyme that breaks the cell wall from within, thus destructing the host cell.
Lysogenic cycle also includes steps of infection, penetration and incorporation of the genetic material. But, after the virus integrates its genetic material it becomes dormant, letting the host multiple and continue its normal activities. Viral genetic material replicates within the host DNA during the host cell's division, so the daughter host cells are infected too. At some point, the virus is triggered, it multiplies and ultimately, destroys the host cells.