Dear Sravanthi actually Core HR & HR generalist are similar but slight difference between the two.
Core HR includes the all HR activities Only like, Recruitment, Performance appraisal, Payroll.....etc.
But in the HR generalist it includes administration like managing sub departments such as house keeping, security and continuous monitoring around the working place, if anything happened in the working place he should immediately respond to that, responsible of Out side the Core HR topics.
The generalist rolls different from type of organization

If you need clarity ask me with an example (like manufacturing firm, service organization .....etc.)


Regards,
Jagadeesh