Is CRM a specific category of software or just whatever holds a contact list

CRM stands for customer relationship management. Strictly, it means one system of record that holds every person and every interaction with them, so any question like "when did we last speak to this tenant and what did we say" has one answer. The loose market usage is what your owner is doing, calling any tool that stores contacts a CRM. A dialer stores phone numbers and logs calls. An email tool stores addresses and logs sends. Neither one is a CRM by itself, because neither can show you the full history of one person in one place.

So you are being asked to do both things. Organize what exists, then decide whether one system should hold it. The test is simple: pick a tenant inquiry from two months ago and try to reconstruct what happened. If you have to open three logins and guess at the order, the records are split and that is why things fall through.

The part that catches people is that a CRM built for sales pipelines and a system built for tenant and maintenance workflow are different products. Sales CRMs are organized around a deal moving through stages toward a close. Property management software is organized around a unit and a lease that continues. Trying to run maintenance tickets through a seller-lead CRM works badly. Ask your owner which problem he actually wants solved, leasing inquiries or maintenance response, because the answer changes what you buy.