I work for a large financial company. We don't build any HFT systems, but we send our orders through various vendor systems and homegrown ones. The typical strategy is to consolidate orders so we aren't placing a bunch of small orders. This is usually done for funds. I believe the retail orders are placed instantly.
Most of the quantitative systems we have do not actually place trades. Instead they provide data to the fund managers or traders and they make the final decision on placing a trade.
It's hard to say if the roles are equivalent. Role responsibilities and structure vary from company to company, even for something that's named the same. The typical trade team structure is something like 1 desk manager, 2-3 traders, and 3-5 analysts. Usually the desk programmer is not from IT, but rather one of the analysts that knows how to code scripts, Python etc. Their scripts are usually some part of the quantitative analysis process, mostly on current or targeted data.
They also use systems developed by IT. The IT systems are bigger and span multiple trade teams. These systems rely more on historical data or market patterns. An example would be a system used by all equity trade desks to identify potential sources of alpha using big data.
So the desk programmer is really more quantitative since they are an analyst whereas the engineers working on the alpha system rely more on input from analysts on what algorithms to implement.
One other thing to mention is that desk operations is a separate type of role that is more like a better version of help desk support.
This is just how my company is structured. I'm sure others are different.