The core difference
An ATS exists to move candidates through a specific opening: application, interview, offer. A recruitment CRM exists to keep a relationship with talent that has no active opening yet: past finalists, people you met at events, referrals you are not ready to place.
When you use each
If you are closing an active opening, you are in ATS mode. If you are building a pipeline for roles you know will open soon, or nurturing strong candidates who did not fit this time, you are in CRM mode.
Why they converge into one tool
Modern tools for agencies usually combine both, because splitting them across two systems recreates the exact problem the ATS solved: duplicated data, no shared history, and strong candidates who fall through the cracks.