what is the difference between trainee adept master parent?

Each stat: apprentice, trainee, adept and master, will make the villager more likley to keep doining the task. But apprentice dosn't really, it's for the kids, and they don't do tasks apprt form picking mushrooms when you tell them too.

and healing people when you tell them to

And some puzzles require a certain level of skill to complete it. (but not parenting...)

A villager who is an adept or master parent will sometimes try to "embrace" when there is room in the population, even if not "checked" for preferring that skills.

I haven't caught a trainee parent doing so without being checked as a preferred skill.

I had a trainee do so while checked on research.

Important to note: If a completly unskilled villager breeds enough, they will become a parent automatically, so watch out if you don't want a sudden population boom.

Just thought I should add that

*********

But it is only the parent who initiates the breeding who gains the skill...

if a male has breeding skill he will attempt to initiate a relatiosnhip, whether or not it is his checked skill

I don't think that is always true. I've had several games with males with a bit of breeding skills that don't initiate the relationship unless it is checked.

Well i had a villgar that had breeding skill and the box was not checked. Belive me, i saw him do it!