I can understand why you didn't get an answer. At least if they are as perplexed as I am about such a marking. I've never heard of an "onothologist gun", and not sure why they would have a special model, or barreled gun? 
I'm also unsure what the "38 SE" might be. I would guess it might be a .38 Short, but not sure on the "E" after 38 S. 
If it was a for some zoologist who specialized in birds, maybe it's some sort of .38 shot for gathering birds? Is it a smoothbore, and do you know the caliber?

Laurie,

I think you've nailed down what it is, but finding documentation for it may be tough.  

Is there a set of initials just in front of the action on the barrel?

From what I've read and seen on Remingtons, the markings you have are:

spl for special order.

Orni  - your guess of ornitholigist gun is probably right.

32 sb is for 32 shot cartridge, smoothbore.  I presume it is in .32 smoothbore?  Is it rimfire, or centerfire?

Some of the guns I have seen marked spl had LLH stamped near the action.  LL Hepburn was the custom shop manager that did special orders.  I've also seen another mark, I think it was KB, but I can't remember exactly.  I may have a rifle so marked in the safe now.  I'll check.

I've seen these small bore shot guns called taxidermists guns in the old catalogs.  Ornitologist gun would be another appropriate term.  In those politically incorrect days, a birder went out, looked for a rare bird, and shot it to bring it back to identify and to prove he had seen it.  Common use of cameras later took some of the fun out of the hobby of bird watching and identification.

dave  

P.S.  BP posted while I was typing, see he volunteered some of the same info.

The Cabildo Museum in New Orleans had a display of JJ Audubon's paintings and tools that he used for taxidermy.
Included was a small gauge flintlock fowling piece purportedly used by Audubon to collect his specimens.

ssdave wrote on Apr 12^th, 2013 at 9:39pm:


That sure makes more sense (SB and not SE) than what I thought the stamp was! I blew it up to try to make out the 2nd stamp, and still didn't see it as a B Dave. Thanks!
Thought the caliber was .38 though?

That's one very cool little rifle... er, shotgun...   Thanks for posting!!

Laurie,

The markings are clearer than they were with the earlier photo so your attempt to modify the earlier photo definitely helped. Is the character to the right of the SB and to the left of the 2 an A or ?

Have you determined what the basic case is that was used for the shot cartridge? 

It's definitely an intriguing #2 variant!

Laurie,

Thanks for the clarification and additional info. 
Makes me wonder how 38 cal CCI shot capsules with #7 1/2 to #9 shot might perform. Could be a lot of fun to find out!