A lot of what you just described is a web developer, not a web designer. And although there is some overlap, generally a designer does not have to deal with the "programming."
Re: term "Architect"
And that's semantics. The person in that role could also be called a software engineer. Software designer/architect/engineer, all pretty close or even the same, depending on who you talk to.
I don't work in the private sector. I work mostly in education with sites that are content heavy and therefore I use the title "Web Content Engineer." People can call it semantics if they want, but there is an important difference.
My job requires that I work closely with educators and also have a strong background in the content (I have never formally studied CS). I work with academics in terms of organizing information into proper sections for websites. Then, the pages are designed and executed by team, which I usually lead.
I also use the word Engineer because often I am presented with a challenge that goes: "OK I want to be able to do this and this with my classroom by MYSELF." So in addition to organizing content on a site, I have to find ways to let the teacher and students interact with it - in an engaging and efficient manner. I install and modify already available software more than I code, but sometimes I have to code because what's out there simply - sucks. One of my larger projects for the summer is to restylize vBulletin. We bought it 5 years ago and the kids loved it but now in version 3, it's too cluttered and the admin interface is atrocious.
So in conclusion, not everything can be boiled down to web developer or web deigner. I prefer using terms like engineer or architect to more accurately describe what I do. Besides job listings also use those words.
And as people talk about medium, realize there's a 3rd factor. You have to balance (1) specialized knowledge - like history in my example or it could be simple business: sales or marketing, (2) design, and (3) development.
That first factor makes you all the more valuable and is a newer development (I find) because companies want to get the max out of their employees. And to distinguish people who can do all 3 as compared to just 2 and 3, we need terms like architects and engineers.