OJTI= on the job training instructor
Checkie= controller assigned the task of performance assessment of other controllers. Initial location-specific 'rating' or endorsement, ongoing annual re-validation etc. ie. the person who says whether or not you will clear the final hurdle and be an ATC.
Safe/unsafe= subjective decision of those who report on your performance (OJTIs, checkies) based on objective tools. ie. can you do the job in all circumstances.