In the past there were specific people and titles for specific jobs ... Analyst, Programmer, Systems Analyst, Tape Librarian, Operator ... etc. but over the years and more simplicity and automation of systems ... companies started to realize they didn't need a dozen people to do separate jobs ... they started to combine them and wanted people who could do all of it.
In Most of the contracts I've been on over the last decade or so, there are No one trick ponies ... the contractors were well versed in End-To-End systems development ... they could go meet with people, see what they want, design, develop, test and deploy the application after user acceptance. so, In today's world, you are more important to be a Jack-Of-All-Trades ... someone who can take a project and do it on their own if needed or work within a team, etc. (with Minimal Supervision).
In the Big Bank Merger I did several years ago ... all of the people I worked with had Multiple Certifications ... from programming languages, Business Analysts, ITIL, Project Manager, CPA, CSM, CPO, etc. Including certified teachers for user training.
"that's more of a PM role, which doesn't seem to exists anymore. "
Project managers are still around, but ... PM roles are now becoming a combination of a PM / BSA (technical background with Agile experience) ... and some certifications for Agile are Certified Scrum Master (CSM) and Certified Product Owner (CPO).
"What type of analyst am I?"
If you are designing and developing stored procedures, triggers, reports, tables, views etc. and implementing them in SQL Server... I would say you are a Programmer / Business Systems Analyst / DBA / Change Management. Which to me is much more valuable than just a Non-Technical BA who does not understand all that stuff. For one person, you can do a lot of stuff and the company saves money on you ... they don't need multiple people.
Don't downplay your technical background ... and remember in your resume, mention that you can communicate to Technical and Non-Technical people.