What is Core HR software? Any experience choosing a software for your business

Hello! I've been tasked with identifying a new core hr software solution to migrate our current HR software. I'm not totally familiar with core HR and how it's different from standard HR software. I want to start my search early and learn as much as I can before making the decision. Can anyone with experience in the Core HR world help me refine my search?

My current shortlist

Rippling: Rippling is an all-in-one platform that seamlessly integrates HR, IT, payroll, and spend management. It enables businesses to manage employee data, benefits, payroll, and even IT device management from a single, unified system. This integration simplifies administrative tasks and ensures consistency across various functions.

BambooHR: BambooHR is a comprehensive HR software solution designed to assist small and medium-sized businesses manage employee data, hiring, onboarding, compensation, and culture. It offers a centralized system that simplifies HR processes and provides valuable insights through reporting and analytics.

Should I expand my search or stick to Rippling or BambooHR? Thanks in advance!