First off, IaaS, PaaS and SaaS are models of cloud service. Cloud computing is, however a very broad term, and these services may not always be used in context of cloud. Below we will discuss the key differences between these services.
SAAS: SOFTWARE AS A SERVICE
SaaS is the most popular form of service today. Interface to applications managed by third parties is provided to clients. Usually no downloads are required for accessing SaaS services as most of them are in-browser apps. Organisations and enterprises do not need to manage beyond their software, such as the resources management. SaaS is primarily targeted at customers of an organisation or end users.
Examples: Google Apps, Salesforce, DropBox, Microsoft 365.
PAAS: PLATFORM AS A SERVICE
PaaS provides framework upon which developers can deploy their code. PaaS gives resources such as the operating system to developers who have freedom to use any programming languages, and can develop, test and deploy applications quickly and inexpensively.
Examples: Google App Engine, Heroku.
IAAS: INFRASTRUCTURE AS A SERVICE
IaaS deliver infrastructure, such as compute, storage and networking. Billing is usually done in terms of utility. Hardware is provided on the cloud, and customers have the ability to access and manage all resources. Users can then deploy their applications or services on top of the infrastructure.
Examples: Amazon Web Services (AWS), Cisco Metapod, Microsoft Azure, Google Compute Engine (GCE).