Am I working in software development industry, or financial services industry?
In the comments on your question, you clarified what you were looking for by saying,
I'm more interested in IF there is a convention of determining which industry I work in and if there is one, what is it? I guess in the end, this is more about "the determination process" than "the determined answer itself"
To me, that's a much more valuable question. It sounds like the point you're struggling with is that some job titles can play support roles in other industries, but also have their own industry category themselves - are these jobs a means to an end, or the end result themselves?
Typically, the convention is to express two categories - a job title, and an industry. So, rather than worrying about if you're in the software industry or the financial services industry, make sure you're distinguishing between title and industry. It's possible to be a software developer in the software industry (i.e. you work for Google) but it's also possible to be a software developer in the financial services industry (you're writing software for a bank or other FI company).
This convention works for a single job, i.e. describing where you're working now (sounds like you are a software developer in the financial services industry!) But when you're writing a resume, or updating a LinkedIn profile, you will typically have a summary at the top, and it's important to use that to describe your career path and not just a single position you happen to be holding at the moment. This leads to a decision you have to make, are you interested in focusing on a specific industry and domain knowledge set, or are you interested in focusing on a specific role?
The emphasis you choose for your summary is important. For recruiters, the first sentence or two on your profile is both more meaningful than the title currently under your name, and it's easier to digest than having to read your entire profile and infer a career path. So, while you have some flexibility in how you describe yourself, you want to make sure you're choosing deliberately.
Many people in services roles like IT will bounce between industries, and will care more about their role than the domain they're in. They may end up with a profile that focuses more on their role(s):
Software developer specializing in web application development, universal design, and mobile applications
Others will want to leverage their domain, and may end up with something more along the lines of,
Enterprise banking application developer and implementer, skilled in home banking and mobile banking platforms
Those two summaries may be the same person, just with different goals.
So - ultimately - you need to consider both industry/domain and job title, but when you're describing yourself, you have a choice in which one you emphasize, based on your career goals.