Terraform throws "groupName cannot be used with the parameter subnet" or "VPC security groups may not be used for a non-VPC launch"

When trying to figure out how to configure a aws_instance with AWS VPC the following errors occur:

* Error launching source instance: InvalidParameterCombination: The parameter groupName cannot be used with the parameter subnet
    status code: 400, request id: []

or

* Error launching source instance: InvalidParameterCombination: VPC security groups may not be used for a non-VPC launch
    status code: 400, request id: []