A KPI is a quantifiable measure used to evaluate how successful an organization/team/ employee, etc. is in meeting objectives for a specific business goal. In its simplest form, a KPI is a form of performance measurement.
A metric is simply a measurement, generally related to a business process. KPIs are metrics related to specific business goals and are generally used to set targets for performance.
Simply put, every KPI is a metric, but not every metric is a KPI.
Some of the most commonly used KPIs in SaaS businesses include ARR/MRR (Annual/Monthly Recurring Revenue (MRR), Churn, CAC (Customer Acquisition Cost), CLV (Customer Lifetime Value, etc).