CDK: Is a framework to model and provision your infrastructure or stack. Stack can consist of a database for ex: DynamoDB, S3 Bucket, Lambda, API Gateway etc. It provides a facility to write code to create an infrastructure in AWS. Also called Infrastructure as code. Check here

SDK: These are the code libraries provided by Amazon in various languages, like Java, Python, PHP, Javascript, Typescript etc. These libraries help interact with AWS services (like creating data in DynamoDB) which you either create through CDK or console. SDKs simplify using AWS services in your application with an API. Check here

AWS SDK is a library primarily to ease the access to the AWS services by handling for you the data (de)serialization, credentials management, failure handling, etc. Perhaps, for specific scenarios, you could use the AWS SDK as the infrastructure as a code tool, however it could be cumbersome as it is not the intended usage of the library.

Based on the https://docs.aws.amazon.com/whitepapers/latest/develop-deploy-dotnet-apps-on-aws/infrastructure-as-code.html, dedicated tools for the IaC are AWS CloudFormation and AWS CDK.

AWS CDK is an abstraction on top of CloudFormation. CDK scripts are in fact transformed to the CloudFormation definitions when scripts are synthesized.

The difference can be best described on an example: Imagine that for each lambda function in your stack you want to create an error CloudWatch alarm and connect to the SNS topic.

With CloudFormation you will either a) need to write a pretty much similar bunch of yaml/json definitions for each lambda function to ensure the monitoring, b) use the nested stack templates, c) use CloudFormation modules.

With CDK you can write a generic code construct - class or method, which can create the alarm for the given lambda function and create the SNS alarm action for given topic.

In other words, CDK helps you generalize and re-use your IaC in a very familiar way to how you develop your business code. The code is shorter and more readable than the CF definitions.

The difference is even more remarkable when you need to set up similar resources in different AWS regions and when you have different AWS account per environment. You can manage all AWS accounts and regions with a single CDK codebase.

I find that the difference for me is that the CDK codifies the CloudFormation JSON/YAML. First response, is great ya okay in code but the benefit on the code side of things is you can write unit testing against the code. Therefore you get to build that sense of security or insurance policy against the provisioned services in the CDK.

There are other ways to test CF, however, with a dev background, this feels more comfortable.