Title is King, once you have it, there's no going back. And i'd definitely add the lead bit to the title on your resume. Since there's a few BA/SA/BSA in here, what does the job entail? Management is my goal, i'd love to learn more of the technical/business needs side.
a BSA and BA are similar kinda the same. BSA is used more so as it relates to IT infrastructure of a company/clients while BA is more used in Software Dev but BA is also used when it comes to Finance, Data Analysis, etc. Pretty much you are the middle man that works with the technical team and are the point of contact for the Non Technical End Users/Clients/Business. So while in a BA/BSA role you will not be doing the technical dirty work, a technical understanding will set you apart from others. A System Analyst is a more technical role than BA as they tend to code depending on situation.
Many times Technical resources aren't the most sociable and only understand the technical specifics and now how these things impact the company on a business scale (as most executives only care about how something impacts their company reputation and cost and can careless about the syntax, how good the code looks, etc). So from a Management Standpoint a BA/BSA has a better shot at becoming a manager, while the Technical counterparts may end up becoming Team SMEs/Consultants who know the system/infrastructure like the back of their hands. In this day and age though you set yourself apart having business and tech knowledge. For example Bill Gates was waaaaay more technical than Steve Jobs but Steve jobs was a business genius and knew enough about the Technical side to do what he needed to do.