in a larger company, the process for getting a website (or piece of new functionality) from idea to online usually involves a lot of different areas
you have someone like a Business Analyst or Requirements Analyst figuring out what it needs to do
you have UX designers making mock ups (usually wireframes) of where the buttons will go, where images should go, where the text should go, that sort of thing
if its part of an existing website or company, the marketing department or UX designers usually have some sort of existing color scheme that will be applied
then you have architects designing how the web site will flow within whatever technologies are being used
where the various tiers are, business logic vs presentation vs storage, and such
an infrastructure or operations team team to set up the servers
backend developers doing the storage portion, DBAs and DB developers if this is a database
front-end programmers designing the presentation, styling, and UI
middle tier programmers doing the business logic
more programmers doing the connective pieces between layers
then it gets built, goes to a testing team, and eventually out the door
in a smaller shop, those roles are still present, its just that fewer people are doing them
so you might have one programmer do the database, and another to do the rest
or single programmer doing everything
but even though the UI programmer is just programming the UI, they are still coding, debugging, and troubleshooting to solve problems that appear in the frontend
similarly the database programmers are coding and debugging issues that appear in the database piece
so pretty much anywhere you go as a programmer, you will be solving problems no matter what