Definition of Infrastructure as a Service
Infrastructure as a Service is a provision model in which an
organization outsources the equipment used to support operations,
including storage, hardware, servers and networking components. The
service provider owns the equipment and is responsible for housing,
running and maintaining it. The client typically pays on a per-use
Characteristics and components of IaaS include:
-Utility computing service and billing model.
-Automation of administrative tasks.
Definition of web hosting
A web hosting service is a type of Internet hosting service that allows individuals and organizations to make their website accessible via the World Wide Web. Web hosts are companies that provide space on a server owned or leased for use by clients, as well as providing Internet connectivity, typically in a data center.
As you can see IaaS offers more functionality and flexibility then web hosting. But at a cost. This chart compares the two nicely (although it by a IaaS provider so take it with a grain of salt).