Since Parse includes a web server, you can interact with it through simple HTTP requests. DynamoDB is just a database, so you will need to directly connect via the AWS SDK or create an API in front of it, possibly using the Gateway and Lambda APIs.
In addition, since Parse is a full-featured Backend as a service, and DynamoDB is just a database, there are some features in Parse that won't be available if you just use DynamoDB directly from the iOS app. For example, to reset a user’s password, you need to send an email to the user. DynamoDB does not have a "password reset" function and cannot send emails directly. You will need to create this function yourself, using something like Lambda and SES.
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