You got a 681 Brother. Simple as that but then I see you're in MA so maybe not so simple due to "registered as".
If inside the crane it's marked 686-1, well, as noted, yours would not be the first to be mismarked, double stamped, etc. But no ifs, ands, or buts, yours is a 4" 681. That thing should be safe to shoot with any sane .357 load you want to put in it. Meaning ANY factory loading will work, and work just fine. As for .38's? Any of those as well so I don't think you have a safety issue.
What I'm curious about is what hoops you might have to jump thru regulatory wise if someone prior to you put the wrong model down on a form. So while not a "safety issue" do you have a "public safety issue"? Inquiring minds want to know.
P.S. Good luck with any hurdles but sheez...how do ya'll deal with all that red tape stuff?