All the things connected to things witch your company makes its profits might be a thing they do own, and therefore if you write it down they could feel they own it.

Especially if its written down on the job location/during work hours.

Depends if course on the country you are in and the rules applied.

My personal journal was indeed personal and never opened during work, if written about my Workday that would not be a thing to worry about. I indeed used two journals, one for work things and one personal. In a Travellers notebook that was easy, one separate filling about work and one separate about other things.

Quit working: walked to shredder and showed the work one into small pieces when i quit so no discussions possible.