Jesse, I know you don’t mean to come off that way. Words are difficult, as they can be easily misinterpreted. Even though there are not any hard and fast definitions to any of these roles, there are some commonly used terms. It is important to stick within those because you will likely be applying for existing positions.
In simple terms, likely no one is going to see your resume and say “hey, lets get budget approval for this this guy”. Instead they will have already gotten budget approval for a design researcher or interaction designer. Your resume will be compared against the job description that they wrote.