What’s the difference between these types of hosting?
On-prem AKA “on-premise” is the traditional way of hosting on-site. The storage, RAM, electricity, networking, operating system, applications, web servers… everything is managed by you. This typically involves multiple system administrators to keep the service running. Examples of these are traditional engineering organizations or development teams.
Infrastructure-as-a-service AKA IaaS is where you manage the platform, applications, and data. The infrastructure is managed for you. Example: Virtual Machines.
Platform-as-a-service is where you manage the applications and data. The platform and infrastructure is managed for you. Example: Azure App Service.
Software-as-a-service is where you manage data or content. The platform, infrastructure, and application is managed for you. Example: Managed WordPress.
Out of these four types of WordPress hosting, both IaaS and PaaS are available on Azure.