I'm sure definitions vary, but I can tell you a bit about what it means at my $DAYJOB employer. For context: we are a Java shop in terms of our backend service development.
Here, a "Cloud Developer" would be expected to have most of the same skills as any Java backend developer: core Java, SQL, RESTful API development with Jersey or Spring, probably some experience with Hibernate or something similar. Some knowledge w/r/t securing API's with OAuth, SAML, etc. would be part of the mix. Then add knowledge of a portion of at least one cloud provider's offerings. We use AWS, so we'd expect somebody to be familiar with using EC2, S3, IAM, probably RDS, maybe DynamoDB, possibly EMR, etc. using both the API and the UI. Then mix in a little bit of "devops'ish" stuff: shell scripting, at least a little exposure to Ansible or Terraform, etc.
We're only just starting to go down the container route, so experience with things like Docker, Kubernetes, ECS, etc. would probably be a "nice to have" right now.
Something approximately like that is how we'd go looking for a "Cloud Developer" with the exact details depending on the experience level of the position. Of course another firm might prefer, say, Azure skills over AWS, or maybe they'd want OpenStack instead. We just happen to be heavily invested in using AWS, although an OpenStack based internal cloud may be in the picture down the line. So that could change the dynamic of what skills we look for.