What is domain
Let us take some theme/subject. It could be grocery delivery, satellites, swallows observations, anything. Let us name this theme "AAA"
domain model for AAA is a "profi IT" word for model for AAA. That's all.
All elements specific to AAA that you'll set in your model, belong to domain. I don't know, why the old good word theme is not used. It is a pity. But the term is already accepted.
So, delivery and suppliers are in your domain. And also much more specific words belonging to grocery. And to bags. And to people's homes - addresses, drive ways in and out - everything that is relevant to your theme.
The domain sets your vocabulary. And that one is really important - you should use the vocabulary used by your clients and not to invent new words, such as "domain" for "theme" :-)
And first you should define your Use case diagram, later- State machine diagram, Deployment diagram, Component diagram, Communication diagram, Sequence/Activity/Time/Interaction Overview diagrams, and at last - class, object and composite structure diagrams. You needn't make all of them, but SOME are necessary.