The HR recruiter's role is to review employement applications for the company, evaluate talent and provide that insight back to the hiring manager (which will in most cases be you--the player). However, they are very important as they can uncover rare talents in each employee that would otherwise fly under the radar.
The HR Trainer is responsible for creating/finding valuable training programs for each company position. These programs would then become available to use by you--the player or AI companies. Trainers also administer training in most cases, and their acumen has a direct impact on how well that training can be received.
The admin role is designed solely to manage your employees wellbeing. The HR admin monitors both employee happiness as well as benefits and other programs that assist in that same goal. Administrators are directly responsible for mitigating the happiness of your entire organization.