SM adopts Halton Arp's discovery of quasar ejection from host galaxies. An active galaxy ejects baby galaxies known as quasars, which then grow into galaxies themselves. Think of an oak tree growing acorns which then drop off and grow into trees themselves. The oak tree only takes a couple dozen years to complete this cycle, a galaxy I'd say takes a couple trillion years.
Big Bang Creationism theorizes that galaxies appeared out of nothing in the aftermath of the Big Bang.
Both are wildly different. One proposes a creation event, the other proposes continual growth and decay. (As a side note, it is also proposed that hydrogen and helium were never "synthesized", but that they are consistently renewed via Alpha and beta decay. I think I mentioned this in an earlier blog post, I'll have to work on it. Can you imagine? Uniting radioactivity with galaxy birth? That's big time!)