They are related, but not quite. Website design outsourcing refers to a task that involves developing a website’s look and feel. It is what you will be doing when you hire a designer. It is important to note that when you outsource web development, you can still do your design work in-house or through another source, such as an in-house designer.
On the other hand, developing a website means coding it to display and function properly across different browsers and devices. Outsourcing web development involves finding someone else to do that for you.
Many companies use internal and external resources for both web development and design.