I feel that if we're saying TNA and Impact are the same despite different management entirely, then we're also going to have to say WCW/JCP are the same.
Which means no, TNA/Impact has not been around longer than WCW/JCP.
That's fair. I was going by Turner years and beyond and the fact that it's tied much closer to its past than WCW was to JCP, or so it feels.
Speaking personally it's close enough to at least always be TNA if only because typing Impact all the time just sucks. Wrestling's all about acronyms idgaf.
You're right about the closeness in time and acronyms, that's for damn sure. That's another fun parallel between Impact and WCW: they were both named after the major show of their predecessors from before purchase.