There is definetely no simple public API or framework for doing this, and doing this is hard.
Some parts of this info possibly could be retreived by your process itslef with some side-ways which will work on some system versions:
There is a launchctl C-based API, which you can try to use to enumerate all
launch daemon/agent tasks and search for your app path/pid. You may
require a root rights for your process for doing this.
Using open
command-line sometimes could be traced with environment
variables it sets for your process.
Running directly from command-line could leave responsible_pid
filled correctly (which is private API from libquarantine, unless you are observing it with Endpoint Security starting from 11.smth version)
All this things, except launchctl API, are not public, not reliable, could be broken at any time by Apple, and may be not sufficient for your needs.
But it is worth to take them a try, because there is nothing better :)
You could potentially distinguish all cases you want using system events monitoring from some other (root-permitted) process you control, possibly adopting Endpoint Security Framework (requires an entitlement from Apple, can't be distributed via AppStore), calling a lot of private APIs and a doing bunch of reversing tricks.
The open resource I could suggest on this topic is here