When seeing this term does it typically stand for modern church? Denominational? Biblical? Is there a set use or is it a general term people use to fit into their narrative?
It's nothing I ever really gave thought about until I saw an article referring to the churches founding fathers, as also the founders of Pentecostalism (John Wesley and Charles Finney). That didn't sit right with me and made me ask.
That's an interesting question... one that I can't say that I've been able to define well in my own thinking.
To me, it seems that many people, throughout many denominations use the term "founding fathers" as if we all know who they're referring to. While I think that for the first few centuries of Christian history, the names are fairly uniform among different denominations today, the list grows increasingly diverse as the years add up. In other words, I believe that it really depends on who you're talking to at the moment.
With the formation of the RCC, circa 350ish AD - Constantine's era and shortly thereafter, things get wildly chaotic. Mainly because, IMHO, the RCC kinda hi-jacked history by insisting that the RCC in-fact existed before it actually existed. They seem to have altered the record, so to speak.
Anyway, because of that, many protestant/reformist denominations (circa 1500's AD), especially those that vehemently opposed the RCC, dismiss "founding fathers" that are associated with the RCC mantle. We tend to throw the baby out with the bath-water.
For me, the idea that there is a "modern church" is really not definable... not for humans. Only God knows who His children are. Therefore, the term "founding fathers", while idiomatic and widely used, is wholly dependent on who you're talking to at the moment - ergo, denominational and a term that people use to fit their narrative.