1. Key Difference 1: Deployment Environment A major difference between AWS CloudFormation and IntelliJ IDEA is their deployment environment. AWS CloudFormation is a cloud service provided by Amazon Web Services (AWS) that helps automate and manage infrastructure as code in a cloud environment. On the other hand, IntelliJ IDEA is an integrated development environment (IDE) primarily used for software development on local machines.

2. Key Difference 2: Purpose AWS CloudFormation is specifically designed for managing and provisioning AWS resources. It enables users to define and manage their infrastructure using templates that can be version-controlled and deployed repeatedly. On the contrary, IntelliJ IDEA is an IDE meant for developing software applications. It provides tools and features to improve the productivity of developers during the software development lifecycle.

3. Key Difference 3: Infrastructure Management AWS CloudFormation is focused on infrastructure management, allowing users to define and provision a wide range of AWS resources such as EC2 instances, S3 buckets, RDS databases, etc., using declarative templates. Conversely, IntelliJ IDEA does not have direct capabilities for managing infrastructure. It is more focused on code editing, debugging, and testing.

4. Key Difference 4: Scalability When it comes to scalability, AWS CloudFormation offers robust scaling capabilities. It allows users to easily scale up or down their AWS resources as per demand. IntelliJ IDEA, being an IDE, does not provide direct scalability features as it is primarily used for local development and testing. Scalability in software applications is usually taken care of using other tools and technologies.

5. Key Difference 5: Collaboration and Integration AWS CloudFormation provides excellent collaboration features, enabling teams to work together on infrastructure-as-code projects. It supports version control systems, resource sharing, and integration with other AWS services. IntelliJ IDEA also offers collaboration capabilities, but they are more focused on code collaboration, code reviews, and integrating with source control systems like Git.

6. Key Difference 6: Cost Model The cost model of AWS CloudFormation is based on the resources provisioned and the duration of their usage. Users are billed for the resources created and managed through CloudFormation. On the other hand, IntelliJ IDEA follows a licensing model where users need to purchase a license based on their usage (usually per developer). The cost of IntelliJ IDEA depends on the edition chosen (Community, Ultimate, etc.) and the duration of usage.

In Summary, AWS CloudFormation is a cloud service for managing and provisioning AWS resources in a declarative and automated manner, whereas IntelliJ IDEA is an IDE for software development with features focused on improving developer productivity. The key differences include deployment environment, purpose, infrastructure management, scalability, collaboration, and cost model.