There are different models of the cloud. We broadly categorize them on the basis of deployment and service.
If we look at the cloud from a deployment perspective, there are three models.
This model of cloud is open to the public. This means that anyone can sign up and subscribe to set up their infrastructure to host their solution. For example, we have AWS, Microsoft Azure, Google Cloud Platform , IBM Cloud (SoftLayer), Alibaba Cloud, and so on.
This model of cloud is specific to an organization that wants to run their workload in a self-provisioned, secure way, internal to the organization. Organizations deploy private clouds using OpenStack, Apache CloudStack, Eucalyptus, OpenNebula, and so on as orchestration, and for hypervisors they are using VMware ESXi, XenServer, Hyper-V, KVM, and so on.
This model of cloud combines the features of both private and public cloud, or you can say it integrates the public cloud and the on-premise hosted cloud. For example, suppose we have an internally deployed OpenStack cloud platform and now we want it to integrate with any of the public clouds. For this, there are multiple tools available that enable you to integrate both clouds and also facilitate you to lift and shift the workload to and fro. Recently, Cisco came up with a product called Cisco CloudCenter (formerly known as CliQr) providing the same facility.
On the basis of service, we categorize clouds into three parts, which we call the SPI model.
In the SPI model, S represents Software as a Service, P represents Platform as a Service, and I represents Infrastructure as a Service.
In this model, an application running on the cloud is offered directly to the end consumer as a service. Being the end consumer, we subscribe the service and start using it. You do not have access to control and manage the infrastructure layer and platform. Here, you do not need to worry about the IT infrastructure, application, and security. In this model, the Software as a Service (SaaS) provider is responsible for managing the underlying infrastructure.
In this model, the cloud provider sets up a platform to develop your application or run your application. For example, AWS provides the relational database service (RDS) service, which is a DBMS service wherein you just need to subscribe the RDS service and dump your database and start using it. You need not worry about infrastructure, OS, and other operational stuff. Platform as a Service (PaaS) services can be accessed using the API too.
IaaS stands for Infrastructure as a Service. In this model of cloud, you can subscribe to the complete infrastructure (networking, computing, and storage) that is required to run your application. Here, you will get the building blocks that you need to assemble to run your application as per your requirement. Suppose you want to run one web application that is developed in PHP and MySQL. To run this on the IaaS platform you need to subscribe to computing, networking, and storage. Now, you will configure each of them to run your application.
As we have now got a fair understanding of the cloud and cloud models, let's see the architecture so that we can correlate it when we start learning about the security aspects:

In the aforementioned architecture, we can see that the base layer of every cloud is a physical server, storage, and network. On top of it, we have installed the Virtualization Layer (hypervisor), which abstracts all the resources.
Before the hypervisor, we have the Orchestration Layer, which communicates with the Virtualization Layer and makes available resource chunks (computing, storage, and network) to be shared among the multiple tenants on demand.
The user logs in to the cloud dashboard to subscribe the resource and starts running their service or application on it.
One thing we can see here is that the Security layer starts from base and goes up until the top. This means that we need to focus on the security aspect at each layer (from the physical layer to the user layer).