According to Wikipedia, this is what a software engineer is. There is also a comparison to related fields, including computer science, which is what both my degrees are in. However, most of the time, my job title has been some type of software engineer.
Regarding algorithms, I don't know offhand if the algorithms classes taught for software engineers require memorization. If they do, by necessity, they can't require too many of them to be memorized. This implies that the practicing software engineer needs to know only but so many algorithms for a job. This has some implications for what a software engineer might reasonably be expected to do in a given situation. If a problem comes up that is outside the scope of the software engineer's knowledge and experience, someone else (a consultant, perhaps?) may be called in to design the algorithm, and possibly develop it as well.
In actuality, I think the type of work I want to do (network protocols and algorithms) falls into the area of computer engineering. In terms of my career history, I think I'm a mixture of computer scientist, computer engineer, software engineer, and system administrator. In the past, this was considered a good thing. It's not so good now. All of those fields have become specialized, and the interviews (which are key to getting the jobs) test for specialization.
What I can do about this isn't so clear. Taking classes and/or teaching myself things I don't know are options, but it's not obvious that either of those will get (and keep) me employed. As Philosophical Geek noted in his post on his Google interview, companies don't tell you why you didn't get the job. There may be good (legal) reasons for this, but it doesn't help people who want to improve themselves so they can get these jobs. It also potentially hurts these companies, especially the ones who say they can't find qualified people.
On a somewhat related note, I've been thinking about taking fall quarter off from chorus and spending more time on my job search. If I was sure some particular set of steps would result in resuscitating my career, I'd be more inclined to take the time off (even though I don't want to). But I don't want to spend the time I'd be otherwise rehearsing and performing (ie. having fun) on fruitless job searching.