It seems I'm dragging you along with me in the IT field, believe me, it's not premeditated. My question - a little broad that I admit - is: when is ITIL used and when is the PMP used? and why rather the PMP and not the ITIL? and vice versa?
This question can go in a lot of different directions, so I will attempt to be brief. ITIL, as you're probably aware is Information Technology Infrastructure Library; and PMP is a Project Management Professional. Though one can be certified in both, normally when one uses "PMP" they are referencing the certification. Are you asking when would the certifications be used? I think what you're asking is when to use the practices within each framework (ITIL or PMP). And the answer is that these are not mutually exclusive. ITIL is a standard around IT services (SLAs, Continuity Management, Security Management, etc), and PMP is a standard on how to manage projects. The projects occur within an across an IT organization which utilizes ITIL. I hope this helps!
In simple words you need PMP to survive during project creation and ITIL to make it survive after delivery.
If you need more details then you need to spend some time looking for the answer to know the processes for each framework.
A PMP is good across all industries where a project management professional is needed. Whereas an ITIL cert is specific to the IT industry. Both are valuable certifications to have and will serve you well. If you plan on remaining in the tech industry it would be beneficial to get ITIL as well as PMP. If you are wanting to branch out into other industries then just go for the PMP.