You need to think like your customer. If you are a subcontractor and your customer is a shop that is buying code, perhaps you can call yourself a coder. If you are selling directly to customers, who are buying websites, you may need to call yourself a web developer.
And, yes, that means that customers will expect the whole package. They don't know how to draw the lines between how the site looks, how the UI works, how the backend works, and how the hosting and the maintenance workflow will work. Those lines can be hard to draw even for experts, and drawing them is your job. Organizing that, and explaining it to them in their terms, is much of what they pay you for. So you'll need to learn to do some graphics and front-end work, or you'll need to learn how to subcontract that, or you'll have to become a subcontractor yourself or otherwise join up with a network of people who can band together to accomplish all the subtasks needed to build and run a site.
And, yes, that means that customers will expect the whole package. They don't know how to draw the lines between how the site looks, how the UI works, how the backend works, and how the hosting and the maintenance workflow will work. Those lines can be hard to draw even for experts, and drawing them is your job. Organizing that, and explaining it to them in their terms, is much of what they pay you for. So you'll need to learn to do some graphics and front-end work, or you'll need to learn how to subcontract that, or you'll have to become a subcontractor yourself or otherwise join up with a network of people who can band together to accomplish all the subtasks needed to build and run a site.