The sub-parts of a standard draw attention to particular aspects of the standard or emphasize that a particular case must be treated. In this case, S-ID.6c draws attention to linear functions particularly. It’s a bit like saying to your child, make sure you pick up everything, and don’t forget to look under the bed. The second is technically a consequence of the first, but you say it anyway.
I’m not sure about the second part of your question because I don’t know what you have in mind when you talk about “using” a standard. Certainly it’s possible to have a task which addresses some but not all aspects of a standard. And yes, you could just say it is related to S-ID.6, without necessarily naming which part or parts.