Some will say that PaaS did have knobs for amount of servers/instances/dynos/whatever but that's a minor detail and the innovation is called autoscaling. No need for an entirely new buzzword. But naming is both hard and exciting so we have "serverless".
What's the difference? PaaS platforms can accept code from a single function (lambda) all the way up to an entire container (knative/cloud run). The scale of code deployed doesn't really change the definition of a platform.
I've seen PaaS more frequently affiliated with services sold to me where the service is bound to a persisted compute resource, and you're always billed for it. There is a always a cpu core running the platform somewhere.
Whereas serverless/Lambda/container service can take the billed cpu to zero when you deem fit. There are still cpus managing and administering, but you have the option to take your utilization that you get billed for to zero, where in the PaaS that I've been sold to, I didn't have that option. YMMV, of course.
Those who don't "get" cloud likely haven't seen one big use case where the costs of cloud services are pretty immaterial: very large organizations with human-dominated change processes. The win here with cloud is the policies and contracts are embedded into the API and access configurations. The speed-up isn't from elastic services, it is eliminating the layers of humans standing between you and the service you want delivered.
If you work in such an organization where you send in a change ticket with the exact Unix commands you want run, and it takes a week for the sysadmins to get around to processing the ticket, the cloud seems lightning-fast by comparison. Then all the scaffolding to set up CI/CD, CMDB, configuration management, secrets store, elastic services, etc. either on-prem or in the cloud doesn't seem nearly so tedious any longer.
Some will say that PaaS did have knobs for amount of servers/instances/dynos/whatever but that's a minor detail and the innovation is called autoscaling. No need for an entirely new buzzword. But naming is both hard and exciting so we have "serverless".