I spent some time looking online for you. I think they are the same. Typically, the "C" in a Ukulele model number designates "Concert." And, that appears to be the case with Brunswick. Incidentally, my Avast anti virus detected and blocked a threat when I tried to go directly to the brunswickguitars.com website. So, be careful.
I'd guess the "BU4" is someone simply saving themselves a bit of typing, they are typically BU4S (Soprano), BU4C (Concert) etc. Note there is also a BU5 range, in "blonde" wood, constructionally identical to the darker instruments. These are my favourites, I have the tenor and the baritone